## WORD PROBLEMS ON DIRECT PROPORTION

Direct proportion is a situation where an increases in one quantity causes a corresponding increases in the other quantity,

Direct proportion is a situation where an decreases in one quantity causes a corresponding decreases in the other quantity.

Problem 1 :

A dozen bananas costs $20. What is the price of 48 bananas?

Let x be the price of 48 bananas.

As number of banana increases, the price of banana will also increase.

It comes under direct proportion.

Doing cross multiplication,

12 ⋅ x = 48 ⋅ 20

x = (48 ⋅ 20)/12

Therefore, the price of 48 bananas is $80.

Problem 2 :

A group of 21 students paid $840 as the entry fee for a magic show. How many students entered the magic show if the total amount paid was $ 1,680?

Let x be the number of students entered the magic show.

As number of student increases, the entry fees will also increase. It comes under direct proportion.

21 ⋅ 1680 = x ⋅ 840

35280 = x ⋅ 840

35250/840 = x

Therefore, 42 students entered the magic show.

Problem 3 :

A birthday party is arranged in third floor of a hotel. 120 people take 8 trips in a lift to go to the party hall. If 12 trips were made how many people would have attended the party?

Let the number of people have attended the party be x.

As number of trips increases, number of people also increases.

120 ⋅ 12 = 8 ⋅ x

1440 = 8 ⋅ x

Therefore, 180 people attended the party in 12 trips.

Problem 4 :

The shadow of a pole with the height of 8 m is 6 m. if the shadow of another pole measured at the same time is 30 m, find the height of the pole?

Let x be the required height of the pole.

As length of shadow increases, height of the pole also increases.

8 ⋅ 30 = 6 ⋅ x

240 = 6 ⋅ x

Therefore, the height of the pole is 40 m.

Problem 5 :

A postman can sort out 738 letters in 6 hours. How many letters can be sorted in 9 hours?

Let x be the required number of letters.

As required time to sort in hours is increases, so, the number of letters is also increases.

738 ⋅ 9 = 6 ⋅ x

6642 = 6 ⋅ x

Therefore, 1107 letters can be sorted in 9 hours.

Problem 6 :

If half a meter of cloth costs $15. Find the cost of 8 1/3 meters of the same cloth.

Let x be the cost of 8 1/3 m of the same cloth.

Length of cloth is increases. So, cost of cloth is also increases.

15 ⋅ (25/3) = x ⋅ 1/2

125 = x ⋅ 1/2

Therefore, the cost of 8 ⅓ m of cloth is $250.

Problem 7 :

The weight of 72 books is 9 kg. What is the weight of 40 such books?

Weight of 72 books = 9 kg.

72 books ----> 9 kg

40 books ----> x kg

Since the number of books increases, the weight of books will also increase. It comes under direct proportion.

Doing cross multiplication, we get

72x = 9(40)

x = 9(40)/72

Weight of 40 books is 5 kg.

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## Direct Proportion Word Problems

Direct Proportion Word Problems - Displaying top 8 worksheets found for this concept.

Some of the worksheets for this concept are Proportions word problems, Answer each question and round your answer to the nearest, Solving proportion word problems, Partitive proportion word problems, Direct variation word problems work, Ratio and proportion common core word problems, Proportions word problems, Solving proportion word problems involving similar figures.

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## 1. Proportions word problems

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## Course: Class 8 > Unit 11

- Recognizing direct & inverse variation
- Recognizing direct & inverse variation: table
- Direct and Inverse proportions 11.2

## Word problems on direct and inverse proportion

- Your answer should be
- an integer, like 6
- a simplified proper fraction, like 3 / 5
- a simplified improper fraction, like 7 / 4
- a mixed number, like 1 3 / 4
- an exact decimal, like 0.75
- a multiple of pi, like 12 pi or 2 / 3 pi

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## Solving Proportions: Word Problems

Ratios Proportions Proportionality Solving Word Problems Similar Figures Sun's Rays / Parts

Many "proportion" word problems can be solved using other methods, so they may be familiar to you. For instance, if you've learned about straight-line equations, then you've learned about the slope of a straight line, and how this slope is sometimes referred to as being "rise over run".

But that word "over" gives a hint that, yes, we're talking about a fraction. And this means that "rise over run" can be discussed within the context of proportions.

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## You are installing rain gutters across the back of your house. The directions say that the gutters should decline katex.render("\\small{ \\bm{\\color{green}{ \\frac{1}{4} }}}", typed01); 1 / 4 inch for every four feet of lateral run. The gutters will be spanning thirty-seven feet. How much lower than the starting point (that is, how much lower than the high end) should the low end of the gutters be?

Rain gutters have to be slightly sloped so the rainwater will drain toward and then down the downspout. As I go from the high end of the guttering to the low end, for every four-foot length that I go sideways, the gutters should decline [be lower by] one-quarter inch. So how much must the guttering decline over the thirty-seven foot span? I'll set up the proportion, using " d " to stand for the distance I'm needing to find.

There is a variable in only one part of my proportion, so I can use the shortcut method to solve.

d = [(37)(1/4)]/4

For convenience sake (because my tape measure isn't marked in decimals), I'll convert this answer to mixed-number form:

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As is always the case with "solving" exercises, we can check our answers by plugging them back into the original problem. In this case, we can verify the size of the "drop" from one end of the house to the other by checking the products of the means and the extremes (that is, by confirming that the cross-multiplications match) of the completed proportion:

(1/4)/4 = 2.3125/37

Converting the "one-fourth" to " 0.25 ", we get:

(0.25)(37) = 9.25

(4)(2.3125) = 9.25

Since the values match, then the proportionality must have been solved correctly, and the solution must be right.

## Biologists need to know roughly how many fish live in a certain lake, but they don't want to stress or otherwise harm the fish by draining or dragnetting the lake. Instead, they let down small nets in a few different spots around the lake, catching, tagging, and releasing 96 fish. A week later, after the tagged fish have had a chance to mix thoroughly with the general population, the biologists come back and let down their nets again. They catch 72 fish, of which 4 are tagged. Assuming that the catch is representative, how many fish live in the lake?

As far as I know, biologists and park managers actually use this technique for estimating populations. The idea is that, after allowing enough time (it is hoped) for the tagged fish to circulate throughout the lake, these fish will then be evenly mixed in with the total population. When the researchers catch some fish later, the ratio of tagged fish in the sample to untagged is representative of the ratio of the 96 fish that they tagged with the total population.

I'll use " f " to stand for the total number of fish in the lake, and set up my ratios with the numbers of "tagged" fish on top. Then I'll set up and solve the proportion:

Because the variable is in only one part of the proportion, I can use the shortcut method to solve.

f = [(96)(72)]/4

This tells me that the estimated population is:

about 1,728 fish

Another type of "proportion" word problem is unit conversion, which looks like this:

## How many feet per second are equivalent to 60 mph?

To complete this exercise, I will need conversion factors, which are just ratios. (If you're doing this kind of problem, then you should have access — in your textbook or in a handout, for instance — to basic conversion factors. If not, then your instructor is probably expecting that you have these factors memorized.)

I'll set everything up in a long multiplication so that the units cancel :

88 feet per second

Take note of how I set up the conversion factors for my multiplicate (above) in not-necessarily-standard ways. For instance, one usually says "sixty minutes in an hour", not "one hour in sixty minutes". So why did I enter the hour-minute conversion factor (in the second line of my computations above) as "one hour per sixty minutes"?

Because doing so lined up the fractions so that the unit of "hours" in my conversion factor would cancel off with the "hours" in the original " 60 miles per hour". This cancelling-units thing is an important technique, and you should review it further if you are not comfortable with it.

## A particular cookie recipe calls for 225 grams of flour for one batch of thirty cookies. Jade would like to make as many cookies as possible for the upcoming block party, and flour is his only constraint (he's got loads of sugar, eggs, etc). If he has 1.206 kilograms of flour, and assuming that all cookies are the same size, approximately how many cookies can he make? (Round to an appropriate whole number.)

I've got two elements here for my proportion: grams of flour and number of cookies. I got to "grams" first when reading the exercise, so I'll put "grams" on top in my proportion.

Since the relationship is given to me in terms of grams, not kilograms, I'll need to convert Jade's on-hand measure to " 1,206 grams, also. I'll use " c " to stand for the number that I'm trying to figure out for "cookies".

(grams)/(cookies): 225/30 = 1206/ c

Since I have an unknown in only one spot in this proportion, I can use the shortcut method to solve.

c = [(1206)(30)]/225

c = 36180/225

Ohhh! Now I see why the instructions said to round to an "appropriate" whole number: Jade can only make whole cookies; the "point-eight" of a cookie will be an undersized niblet that he'll eat before heading to the party.

While normally I'd round this number up to get my whole-number answer, in this case I need to round down ; in other words, in this context (namely, of all the cookies being the same size), I have to ignore the fractional portion (that is, the point-eight decimal part) to get the desired answer.

160 cookies

## Kumar lives in Croatia, and is visiting relatives in India. The current exchange rate is one Euro ( €1 ) to 80.45 Indian rupees ( ₹80.45 ). He wants to buy a gift for them, which costs ₹3,759 . How many Euros will this gift cost him? (State your answer accurate to two decimal places.)

They've given me an exchange rate, which is, effectively, just another conversion factor, like the "miles per hour" exercise above. So I'll set up my proportion, with Euros on top, and will use e to stand for the number of Euros he'll need.

(Euros)/(Rupees): 1/80.45 = e /3759

I'll use the shortcut method to solve:

e = [(3759)(1)]/80.45

e = 46.72467371...

Rounding to two decimal places, Kumar will be spending:

€46.72

Other than for the rate-conversion exercise above, we've been able to solve all of the proportions by the shortcut method. You will likely find this to be the case in your homework, also. But it is always possible that you'll get a question where you'll be better off using cross-multiplication instead.

## George has heard from two different sources about the pay range at a particular company. One source says that the ratio of lowest pay to highest pay is 3 : 7 . The other source says that the top earner annually makes about $57,000 more than the lowest earner. What are the approximate salaries for the highest and lowest earners? (Round to the nearest thousand.)

I know that the ratio is 3 : 7 , so I'll be using the fraction 3/7 for one side of my proportion. If the lowest pay rate, in thousands of dollars, is L , then the highest is L + 57 . My proportion is:

(lowest)/(highest): 3/7 = L /( L + 57)

Because there are variables in two of the parts of this proportion, the shortcut method won't be as useful as cross-multiplication to clear all the fractions. So I'll cross-multiply:

3/7 = L /( L + 57)

3( L + 57) = 7 L

3 L + 171 = 7 L

Remembering that I dropped the trailing zeroes and am counting by thousands, the above number means that the lowest salary is (rounded to the nearest thousand) approximately $43,000 . Then the highest salary, being around $57K more, is approximately $100,000 .

lowest: $43,000 highest: $100,000

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## Direct Proportion

Direct proportion is a mathematical comparison between two numbers where the ratio of the two numbers is equal to a constant value. The proportion definition says that when two ratios are equivalent, they are in proportion. The symbol used to relate the proportions is "∝". Let us learn more about direct proportion in this article.

## Direct Proportion Definition

The definition of direct proportion states that "When the relationship between two quantities is such that if we increase one, the other will also increase, and if we decrease one the other quantity will also decrease, then the two quantities are said to be in a direct proportion". For example, if there are two quantities x and y where x = number of candies and y = total money spent. If we buy more candies, we will have to pay more money, and we buy fewer candies then we will be paying less money. So, here we can say that x and y are directly proportional to each other. It is represented as x ∝ y. Direct proportion is also known as direct variation.

Some real-life examples of direct proportionality are given below:

- The number of food items is directly proportional to the total money spent.
- Work done is directly proportional to the number of workers.
- Speed is in direct proportion to the distance w.r.t a fixed time.

## Direct Proportion Formula

The direct proportion formula says if the quantity y is in direct proportion to quantity x, then we can say y = kx, for a constant k. y = kx is also the general form of the direct proportion equation.

- k is the constant of proportionality .
- y increases as x increases.
- y decreases as x decreases.

## Direct Proportion Graph

The graph of direct proportion is a straight line with an upward slope . Look at the image given below. There are two points marked on the x-axis and two on the y-axis, where (x) 1 < (x) 2 and (y) 2 < (y) 2 . If we increase the value of x from (x) 1 to (x) 2 , we observe that the value of y is also increased from (y) 1 to (y) 2 . Thus, the line y=kx represents direct proportionality graphically.

## Direct Proportion Vs Inverse Proportion

There are two types of proportionality that can be established based on the relation between the two given quantities. Those are direct proportion and inverse proportional. Two quantities are directly proportional to each other when an increase or decrease in one leads to an increase or decrease in the other. While on the other hand, two quantities are said to be in inverse proportion if an increase in one quantity leads to a decrease in the other, and vice-versa. The graph of direct proportion is a straight line while the inverse proportion graph is a curve. Look at the image given below to understand the difference between direct proportion and inverse proportion.

## Topics Related to Direct Proportion

Check these interesting articles related to the concept of direct proportion.

- Constant of Proportionality
- Inversely Proportional
- Percent Proportion

## Direct Proportion Examples

Example 1: Let us assume that y varies directly with x, and y = 36 when x = 6. Using the direct proportion formula, find the value of y when x = 80?

Using the direct proportion formula, y = kx Substitute the given x and y values, and solve for k. 36 = k × 6 k = 36/6 = 6 The direct proportion equation is: y = 6x Now, substitute x = 80 and find y. y = 6 × 80 = 480

Answer: The value of y is 480.

Example 2: If the cost of 8 pounds of apples is $10, what will be the cost of 32 pounds of apples?

It is given that, Weight of apples = 8 lb Cost of 8 lb apples = $10 Let us consider the weight by x parameter and cost by y parameter. To find the cost of 32 lb apples, we will use the direct proportion formula. y=kx 10 = k × 8 (on substituting the values) k = 5/4 Now putting the value of k = 5/4 when x = 32 we have, The cost of 32 lb apples = 5/4 × 32 y =5×8 y = 40

Answer: The cost of 32 lb apples is $40 .

Example 3: Henry gets $300 for 50 hours of work. How many hours has he worked if he got $258?

Solution: Let the amount received by Henry be treated as y and the number of hours he worked as x. Substitute the given x and y values in the direct proportion formula, we get, 300 = k × 50

⇒ k=300/50 k = 6 The equation is: y = 6x. Now, substitute y = 258 and find x. 258 = 6 × x

⇒ x = 258/6 = 43 hours Therefore, if Henry got $258, he worked for 43 hours.

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## Direct Proportion Practice Questions

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## FAQs on Direct Proportion

What is direct proportion in maths.

Two quantities are said to be in direct proportion if an increase in one also leads to an increase in the other quantity, and vice-versa. For example, if a ∝ b, this implies if 'a' increases, 'b' will also increase, and if 'a' decreases, 'b' will also decrease.

## What Is the Symbol ∝ Denotes in Direct Proportion Formula?

In the direct proportion formula, the proportionate symbol ∝ denotes the relationship between two quantities. It is expressed as y ∝ x, and can be written in an equation as y = kx, for a constant k.

## What is Direct Proportion and Inverse Proportion?

Direct proportion, as the name suggests, indicates that an increase in one quantity will also increase the value of the other quantity and a decrease in one quantity will also decrease the value of the other quantity. While inverse proportion shows an inverse relationship between the two given quantities. It means an increase in one will decrease the value of the other quantity and vice-versa.

## How do you Represent the Direct Proportional Formula?

The direct proportional formula depicts the relationship between two quantities and can be understood by the steps given below:

- Identify the two quantities which vary in the given problem.
- Identify the variation as the direct variation .
- Direct proportion formula: y ∝ kx.

## What is a Direct Proportion Equation?

The equation of direct proportionality is y = kx, where x and y are the given quantities and k is any constant value. Some examples of direct proportional equations are y = 3x, m = 10n, 10p = q, etc.

## How to Solve Direct Proportion Problems?

To solve direct proportion word problems, follow the steps given below:

- Make sure that the variation is directly proportional.
- Form an equation in terms of y = kx and find the value of k base on the given values of x and y.
- Find the unknown value by putting the values of x and the known variable.

## How to Show Relationship Between Two Quantities Using Direct Proportion Formula?

The directly proportional relationship between two quantities can figure out using the following key points.

- Identify the two quantities given in the problem.
- If x/y is constant then the quantities have a directly proportional relationship.

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Proportion word problems

It is very important to notice that if the ratio on the left is a ratio of number of liters of water to number of lemons, you have to do the same ratio on the right before you set them equal.

## More interesting proportion word problems

Check this site if you want to solve more proportion word problems.

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Direct Variation

## Direct Variation or Direct Proportion:

Examples on direct variation or direct proportion:.

(i) The cost of articles varies directly as the number of articles. (More articles, more cost) (ii) The distance covered by a moving object varies directly as its speed. (More speed, more distance covered in the same time) (iii) The work done varies directly as the number of men at work. (More men at work, more is the work done in the same time) (iv) The work done varies directly as the working time. (More is the working time, more is the work done)

## Solved worked-out problems on Direct Variation:

1. If $ 166.50 is the cost of 9 kg of sugar, how much sugar can be purchased for $ 259? Solution: For $ 166.50, sugar purchased = 9 kg For $ 1, sugar purchased = 9/166.50 kg [less money, less sugar] For $ 259, sugar purchased = {(9/166.50) × 259} kg [More money, more sugar] = 14 kg. Hence, 14 kg of sugar can be purchased for $ 259.

2. If one score oranges cost $ 45, how many oranges can be bought for $ 72? Solution: For $ 45, number of oranges bought = 20 For $ 1, number of oranges bought = 20/45 [less money, less oranges] For $ 72, number of oranges bought = {(20/45) × 72} [More money, more oranges] = 32. Hence, the number of oranges bought for $ 72 is 32.

3. If a car covers 82.5 km in 5.5 litres of petrol, how much distance will it cover in 13.2 litres of petrol? Solution: In 5.5 litres of petrol, distance covered = 82.5 km In 1 litre of petrol, distance covered = 82.5/5.5 km [less petrol, less distance] In 13.2 litres of petrol, distance covered = {(82.5/5.5) × 13.2} km [More petrol, more distance] = 198 km. Hence, the car covers 198 km in 13.2 litres of petrol.

## More examples on Direct Variation word problems:

4. If 5 men or 7 women can earn $ 875 per day, how much would 10 men and 5 women earn per day? Solution: 5 men = 7 women ⇒ 1 man = 7/5 women ⇒ 10 men = (7/5 × 10) women = 14 women ⇒ (10 men + 5 women) ≡ (14 women + 5 women) = 19 women. Daily earning of 7 women = $ 875 Daily earning of 1 woman = $ (875/7) [less women, less earning] Daily earning of 19 women = $ (875/7 × 19) [More women, more earning] = $ 2375 Hence, 10 men and 5 women earn $ 2375 per day.

5. If 3 men or 4 women earn $ 480 in a day, find how much will 7 men and 11 women earn in a day? Solution: One day earning of 3 men = $ 480 One day earning of 1 man = $ (480/3) [less men, less earning] One day earning of 7 men = $ (480/3 × 7) [more men, more earning] = $ 1120 One day earning of 4 women = $ 480 One day earning of 1 woman = $ (480/4) [less women, less earning] One day earning of 11 women = $ (480/4 x 11) [More women, more earning] = $ 1320 One day earning of 7 men and 11 women = $ (1120 + 1320) = $ 2440.

6. The cost of 16 packets of salt, each weighing 900 grams is $ 84. What will be the cost of 27 packets of salt, each weighing 1 kg? Solution: Cost of 16 packets, each weighing 9/10 kg = $ 84 Cost of 16 packets, each weighing 1 kg = $ (84 × 10/9) [more weight per packet, more cost] Cost of 1 packet, each weighing 1 kg = $ (84 × 10/9 × 1/16) [less packets, less cost] Cost of 27 packets, each weighing 1 kg = $ (84 × 10/9 × 1/16 × 27) = $ (315/2) = $ 157.50 [more packets, more cost] Hence, the cost of 27 packets, each weighing 1 kg is $ 157.50.

7. If the wages of 15 workers for 6 days are $ 9450, find the wages of 19 workers for 5 days. Solution: Wages of 15 workers for 6 days = $ 9450 Wages of 1 worker for 6 days = $ (9450/15) [less workers, less wages] Wages of 1 worker for 1 day = $ (9450/15 × 1/6) [less days, less wages] Wages of 19 workers for 1 day = $ (9450 × 1/6 × 19) [more workers, more wages]

Wages of 19 workers for 5 day = $ (9450 × 1/6 × 19 × 5) [more workers, more wages] = $ 9975 Hence, the wages of 19 workers for 5 days = $ 9975. Direct Variation

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## Ratio and Proportion Word Problems

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## SOLVING DIRECT AND INVERSE PROPORTION WORD PROBLEMS

Problem 1 :

Karen earns $28.50 for working 6 hours. If the amount m she earns varies with h the number of hours she works, how much she earns for working 10 hours?

It comes under direct proportion.

28.50 ⋅ 10 = x ⋅ 6

x = (28.50 ⋅10) / 6

She is earning $47.5 for 10 hours.

Problem 2 :

A bottle of 150 vitamins costs $5.25. If the cost varies directly with the number of vitamins in the bottle, what should a bottle of 250 vitamins cost?

Let x be the cost of 250 vitamins bottle.

5.25 ⋅ 250 = x ⋅ 150

x = (5.25 ⋅ 250) / 150

x = 1312.5/150

So, cost of 250 vitamins bottle is $8.75.

Problem 3 :

For a fixed number of miles, the gas mileage of a car (miles/gallon) varies inversely with the number of gallons. Stephen's truck averaged 24 miles per gallon and used 750 gallons of gas in one year. If the next year, to rive the same number of miles, Stephen drove a compact car averaging 39 miles per gallon, how many gallons of gas would he use?

It comes under inverse proportion.

24 ⋅ 750 = 39 ⋅ x

x = (24 ⋅ 750)/39

x = 461.5 gallons

So, he is using 461.5 gallons of gas.

Problem 4 :

Wei received $55.35 in interest on a $1230 in her bank account. If the interest varies directly with the amount deposited, how much would Wei receive for the same amount of time if she had $2000 in her account?

1230 ⋅ x = 2000 ⋅ 55.35

x = (2000 ⋅ 55.35)/1230

So, he will earn the interest of $90.

Problem 5 :

The number of gallons g of fuel used on a trip varies directly with the number of miles m traveled. If a trip of 270 miles required 12 gallons of fuel, how many gallons are required for a trip of 400 miles?

12 ⋅ 400 = x ⋅ 270

x = (12 ⋅ 400) / 270

x = 17.7 gallons

So, 17.7 gallons is required for a trip of 400 miles.

Problem 6 :

The time it takes to travel a fixed distance varies inversely with the speed traveled. If it takes Pam 40 minutes to bike to her fishing spot at 9 miles per hour, how long will it take her if she rides at 12 miles per hour?

Here the distance to be covered in both cases is the same.

9 ⋅ 40 = 12 ⋅ x

x = (9 ⋅ 40) / 12

x = 30 minutes

So, he can cover the same distance in 30 minutes.

Problem 7 :

The time needed to paint a fence varies directly with the length of the fence. If it takes 5 hours to paint 200 feet of fence, how long will it take to paint 500 feet of fence?

200 ⋅ x = 500 ⋅ 5

x = (500 ⋅ 5)/200

x = 2500/200

x = 12.5 hrs

So, it will take 12.5 hours.

Problem 8 :

The number of bricks laid varies directly with the amount of time spent. If 45 bricks are laid in 65 minutes, how much time would it take to lay 500 bricks?

1 bricks are laid = 65/45 = 13/9 min

Then 500 bricks are laid = (13/9 × 500) min

= (6500/9) × 60 min

= 12 hr 3 min

So, it will take 12 hr 3 min to lay 500 bricks.

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Therefore, 1107 letters can be sorted in 9 hours. Problem 6 : If half a meter of cloth costs $15. Find the cost of 8 1/3 meters of the same cloth. Solution : Let x be the cost of 8 1/3 m of the same cloth. Length of cloth is increases. So, cost of cloth is also increases. It comes under direct proportion.

Here we will learn about direct proportion, including what direct proportion is and how to solve direct proportion problems. We will also look at solving word problems involving direct proportion. ... Money is used in many direct proportion word problems. If an answer is 5.3 you may be tempted to write it as £5.3, but the correct way of ...

Proportion Word Problems. 3) One cantaloupe costs $2. How many cantaloupes can you buy for $6? 5) Shawna reduced the size of a rectangle to a height of 2 in. What is the new width if it was originally 24 in wide and 12 in tall? 7) Jasmine bought 32 kiwi fruit for $16. How many kiwi can Lisa buy if she has $4? 9) One bunch of seedlees black ...

This video shows how to solve inverse proportion questions. It goes through a couple of examples and ends with some practice questions. Example 1: A is inversely proportional to B. When A is 10, B is 2. Find the value of A when B is 8. Example 2: F is inversely proportional to the square of x. When A is 20, B is 3. Find the value of F when x is 5.

Direct Proportion Word Problems - Displaying top 8 worksheets found for this concept. Some of the worksheets for this concept are Proportions word problems, Answer each question and round your answer to the nearest, Solving proportion word problems, Partitive proportion word problems, Direct variation word problems work, Ratio and proportion ...

Proportion word problems. Google Classroom. Sam used 6 loaves of elf bread on an 8 day hiking trip. He wants to know how many loaves of elf bread ( b) he should pack for a 12 day hiking trip if he eats the same amount of bread each day.

In notation, direct proportion is written as. y ∝ x. Example 1: If y is directly proportional to x and given y = 9 when x = 5, find: a) the value of y when x = 15. b) the value of x when y = 6. Solution: a) Using the fact that the ratios are constant, we get. 95 9 5 = y 15 y 15.

WORD PROBLEMS ON DIRECT AND INVERSE PROPORTION. A direct proportion shows the direct the relation between two quantities. If one quantity increases, then another will also increase. If one quantity decreases, then another will also decrease. An inverse proportion shows inverse or indirect relation between two quantities.

Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. ... Word problems on direct and inverse proportion. Math > Class 8 > Direct and Inverse proportions > ... Word problems on direct and inverse proportion. Google Classroom.

Purplemath. Many "proportion" word problems can be solved using other methods, so they may be familiar to you. For instance, if you've learned about straight-line equations, then you've learned about the slope of a straight line, and how this slope is sometimes referred to as being "rise over run".. But that word "over" gives a hint that, yes, we're talking about a fraction.

Lesson Plan: Proportion Word Problems Mathematics • 7th Grade. Lesson Plan: Proportion Word Problems. This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to find an unknown term in a proportion and solve word problems on proportions involving fractions and decimals.

In this lesson, you will learn the different proportion problems. The set-up of the different proportion problems and the steps on how to solve these problem...

To solve direct proportion word problems, follow the steps given below: Identify the two quantities which vary in the given problem. Make sure that the variation is directly proportional. Form an equation in terms of y = kx and find the value of k base on the given values of x and y.

Cross product is usually used to solve proportion word problems. If you do a cross product, you will get: 4 × x = 3 × 8 4 × x = 24. Since 4 × 6 = 24, x = 6 6 liters should be mixed with 8 lemons. More interesting proportion word problems Problem # 2 A boy who is 3 feet tall can cast a shadow on the ground that is 7 feet long.

IXL's SmartScore is a dynamic measure of progress towards mastery, rather than a percentage grade. It tracks your skill level as you tackle progressively more difficult questions. Consistently answer questions correctly to reach excellence (90), or conquer the Challenge Zone to achieve mastery (100)! Learn more. 0.

Direct Variation or Direct Proportion: Two quantities are said to vary directly if the increase (or decrease) in one quantity causes the increase (or decrease) in the other quantity. ... More examples on Direct Variation word problems: 4. ... In 2nd Grade number Worksheet we will solve the problems on 3-digit numbers, before, after and between ...

If we replace the proportionality sign with the equal sign, the equation changes to: a= kb a = kb. where k is called a constant of proportionality. Many real-life situations have direct proportionalities, for example: The work done is directly proportional to the number of workers. The cost of food is directly proportional to weight.

Math worksheets: Proportions word problems. Below are grade 6 math worksheets with proportions word problems. Open PDF. Worksheet #1 Worksheet #2. Worksheet #3. Become a Member. These worksheets are available to members only. Join K5 to save time, skip ads and access more content.

Direct and Indirect Proportion Lessonhttps://www.youtube.com/watch?v=tQSnXVR6368&t=1230sEasiest way to learn how to solve equationshttps://www.youtube.com/wa...

Ratio and proportion Solving direct and inverse proportion problems Examples: 1. y is directly proportional to x, where y is 10, x is 2. Find the formula and solve when y is 25. 1. y is inversely proportional to x, where y is 10, x is 2. Find the formula and solve when y is 25. Show Step-by-step Solutions

SOLVING DIRECT AND INVERSE PROPORTION WORD PROBLEMS. Problem 1 : Karen earns $28.50 for working 6 hours. If the amount m she earns varies with h the number of hours she works, how much she earns for working 10 hours? Solution: It comes under direct proportion. 28.50 ⋅ 10 = x ⋅ 6. x = (28.50 ⋅10) / 6. x = 285/6.

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2. Write down the proportion. The written proportion should be in the form "x is directly proportional to y". 3. Find a pair of values that illustrates the proportion. For example, if x = 2 and y = 4, this is an example of a direct proportion since x is directly proportional to y. 4. Use the given pair of values to calculate the ratio.