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Chapter 6: Problem 1

A company that manufactures optical products estimated that three out of five people in North America wear eyeglasses. The population of North America was projected to be about 540 million in 2010 . Use a proportion to estimate the number of people in North America who were expected to wear eyeglasses in 2010 .

Short Answer

Expert verified
Answer: Approximately 324 million people in North America wore eyeglasses in 2010.

Step by step solution

01

Write down the known facts

We are given that three out of five people in North America wear eyeglasses, which can be represented as a fraction: \(\frac{3}{5}\). Additionally, the population of North America was estimated to be 540 million in 2010.
02

Set up a proportion

A proportion is an equation representing ratio relationships between two quantities. Let x be the estimated number of eyeglass wearers in 2010. The proportion between eyeglass wearers (3) and total people (5) should be equal to the proportion between x and the total number of people in North America (540 million): \[\frac{3}{5} = \frac{x}{540\text{ million}}\]
03

Solve the proportion for x

To solve for x, cross-multiply and then divide by the common factor: \[3 * 540\text{ million} = 5 * x\] Now divide both sides by 5 to isolate x: \[x = \frac{3 * 540\text{ million}}{5}\]
04

Calculate the number of eyeglass wearers in North America in 2010

Use the proportion found in step 3 to calculate the number of eyeglass wearers: \[x = \frac{3 * 540\text{ million}}{5} = 324\text{ million}\]
05

Interpret the result

The estimated number of people in North America who wore eyeglasses in 2010 was 324 million.

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