## Solving proportion word problems

The Crayola crayon company can make 2400 crayons in 4 minutes. How many crayons can they make in 15 minutes?

To solve this problem we begin by making a table and filling in the given information.

 crayons minutes 2400 4 x 15

We put "x" under crayons because we don't know how many crayons are made in 15 minutes.

Now solve the proportion:

$\frac{2400}{x}=\frac{4}{15}$

$x=9000\mbox{ crayons}$

A typist can type 120 words in 100 seconds. At that rate, how many seconds would it take her to type 258 words?

To solve this problem we begin by making a table and filling in the given information.

 words seconds 120 100 258 x

We put "x" under seconds because we don't know how many seconds it takes to type 258 words.

Now solve the proportion:

$\frac{120}{258}=\frac{100}{x}$

$x=215\mbox{ seconds}$

Example 1

A can of tomato paste weighs 16 ounces and/or 452 grams. This depends on whether you use English measurement or SI.
Make a ratio table to determine the number of ounces in a kilogram (1000 grams).

 Ounces Grams 16 452 x 1000

$\frac{16}{x}=\frac{452}{1000}$

$16\cdot~1000\,=\,452\cdot~x$

$16000\,=\,452\cdot~x$

$35.398\,=\,x$

This means there are about 35.4 ounces in 1 kilogram.

Example 2

Measuring miles on the ocean (nautical miles) is different from "normal" miles on land (statute miles). In fact, 100 nautical miles is equal to 115 statute miles.

If you plan on going 92 statute miles, how many nautical miles would you have to travel?

 Nautical Statute 100 115 x 92

$\frac{100}{x}=\frac{115}{92}$

$100\cdot~92\,=\,115\cdot~x$

$9200\,=\,115\cdot~x$

$80\,=\,x$

This means there are 80 nautical miles for every 92 statute miles.

# Self-Check

Q1: A company can buy packages of 500 sheets of paper for \$4. At that rate, how much paper can be bought for \$2000? [show answer]

Q2: Mixing 4 ml of red paint and 15 ml of yellow paint makes orange paint. How much red would be needed if you use 100 ml of yellow paint? [show answer]

Q3: A fast typist can type 120 words in 100 seconds. In 180 seconds, how many words could be typed? [show answer]