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 basic mathematics image

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 or 4/3= 8/x or 3/x = 4/8 or x/3 = 8/4

It is very important that you notice that if you do a ratio of number of liters of water to number of lemons in the first fractions, you have to do the same ratio in the second fraction before you set them equal. On the other hand, if you do a ratio of number of lemons to number of liters of water in the first fraction, you have to do the same ratio for the second fraction.

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

if you do a cross product, you will get 4 times x = 3 times 8

4 times x = 24. Thus x = 6

Problem # 2

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

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

We will solve the first one:

3/900 = x/300

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

900 = x times 900. Thus x = 1 because 1 times 900 = 900.

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