# Proportion word problems

There are lots of situations that can create proportion word problems. We will illustrate these situations with some examples

Problem # 1

Mix 3 liters of water with 4 lemons to make lemonade. How many liters of water are mixed with 8 lemons.

Set up the ratios, but make sure that the two ratios are written in the same order.

For example, all the followings can be used to solve this problem:

Let x be number of liters of water.

 3 / 4 =     x / 8 , 4 / 3 =     8 / x , 3 / x =     4 / 8 , x / 3 =     8 / 4 ,
 3 / 4 = x / 8 , 4 / 3 = 8 / x , 3 / x = 4 / 8 , x / 3 = 8 / 4

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.

Look carefully and you will see that this is what the first proportion does.

However, the second proportion focuses on a ratio of number of lemons to number of liter of water

 Number of lemons / Number of liters of water =    Number of lemons / Number of liters of water

When solving proportion word problems, make sure it is set up correctly. Once you set up your proportion correctly, all you have to do if to replace values that you know and use an x or any other variable for the value you don't know

Let us solve the second proportion. I already showed you how to solve a proportion. If you do not remember, go to solving proportions

 4 / 3 =       8 / x

 # of lemons / # of liters of water =    # of lemons / # of liters of water

When solving proportion word problems, make sure it is set up correctly. Once you set up your proportion correctly, all you have to do if to replace values that you know and use an x or any other variable for the value you don't know

Let us solve the second proportion. I already showed you how to solve a proportion. If you do not remember, go to solving proportions

 4 / 3 =       8 / x

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

Problem # 2

A boy who is 3 feet tall can cast a shadow on the ground that is 7 feet long. How tall is a man who can cast a shadow that is 14 feet long?

Set up the proportion by doing ratios of height to length of shadow

 Height of boy / Length of shadow =          Height of man / Length of shadow

Replace the known values and use H for the unknown height of the man

 3 / 7 =    H / 14

Cross multiply

3 × 14 = 7 × H

42 = 7 × H

Since 7 × 6 = 42, H = 6

The man is 6 feet tall

Problem # 3

3 gallons of paint cover 900 square feet. How many gallons will cover 300 square feet?

 3 / 900 =     x / 300 900 / 3 =     300 / x 3 / x =     900 / 300 x / 3 =     300 / 900

We will solve the first one:

 3 / 900 =       x / 300

Doing cross product, will give you 3 × 300 = x × 900

900 = x × 900. Thus x = 1 because 1 × 900 = 900.

Problem # 4: Firefighter math and proportion

A firefighter truck can hold 3000 gallons of water. A firefighter can deliver 160 gallons of water every 2 minutes.

1. How much water will be delivered in 10 minutes?

2. How long will it take for the firefighter to empty the tank

1. Set up a proportion by doing ratios of number of gallons to time it takes

 Number of gallons / Time it takes =          Number of gallons / Time it takes

Replace the known values and use G to represent the numbers of gallons in 10 minutes

 160 / 2 =     G / 10

Cross multiply

160 × 10 = 2 × G

1600 = 2 × G

Since 2 × 800 = 1600, G = 800

800 gallons of water will be delivered in 10 minutes

2. Set up a proportion by doing ratios of number of gallons to time it takes

 Number of gallons / Time it takes =          Number of gallons / Time it takes

Replace the known values and use T to represent the time it takes to deliver 3000 gallons

 160 / 2 =     3000 / T

Cross multiply

160 × T = 2 × 3000

160 × T = 6000

Divide 6000 by 160 to get T. 6000 divided by 160 = 37.5

T = 37.5 or 37 minutes and 30 seconds

I welcome any questions about these proportion word problems if you have any

 Height of boy / Length of shadow =          Height of man / Length of shadow

Replace the known values and use H for the unknown height of the man

 3 / 7 =    H / 14

Cross multiply

3 × 14 = 7 × H

42 = 7 × H

Since 7 × 6 = 42, H = 6

The man is 6 feet tall

Problem # 3

3 gallons of paint cover 900 square feet. How many gallons will cover 300 square feet?

 3 / 900 = x / 300 , 900 / 3 = 300 / x , 3 / x = 900 / 300 , x / 3 = 300 / 900

We will solve the first one:

 3 / 900 =       x / 300

Doing cross product, will give you 3 × 300 = x × 900

900 = x × 900. Thus x = 1 because 1 × 900 = 900.

Problem # 4: Firefighter math and proportion

A firefighter truck can hold 3000 gallons of water. A firefighter can deliver 160 gallons of water every 2 minutes.

1. How much water will be delivered in 10 minutes?

2. How long will it take for the firefighter to empty the tank

1. Set up a proportion by doing ratios of number of gallons to time it takes

 # of gallons / Time it takes =          # of gallons / Time it takes

Replace the known values and use G to represent the numbers of gallons in 10 minutes

 160 / 2 =     G / 10

Cross multiply

160 × 10 = 2 × G

1600 = 2 × G

Since 2 × 800 = 1600, G = 800

800 gallons of water will be delivered in 10 minutes

2. Set up a proportion by doing ratios of number of gallons to time it takes

 # of gallons / Time it takes =          # of gallons / Time it takes

Replace the known values and use T to represent the time it takes to deliver 3000 gallons

 160 / 2 =     3000 / T

Cross multiply

160 × T = 2 × 3000

160 × T = 6000

Divide 6000 by 160 to get T. 6000 divided by 160 = 37.5

T = 37.5 or 37 minutes and 30 seconds

I welcome any questions about these proportion word problems if you have any

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