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.
Let x be number of liters of water. All the followings can be used to solve this problem:
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.
Take a closer look, and you'll see that the first proportion maintains the original ratio of liters of water to lemons. In contrast, the second proportion reverses the ratio, focusing on the number of lemons per liter of water as shown below.
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.
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. 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.
Replace the known values and use H for the unknown height of the man.
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?
We will solve the first one:
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
Replace the known values and use G to represent the numbers of gallons in 10 minutes
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
Replace the known values and use T to represent the time it takes to deliver 3000 gallons.
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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