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A certain disease affects 9 out of every 10,000 Americans. In a city of 4.5 million people, how...

Question:

A certain disease affects 9 out of every 10,000 Americans. In a city of 4.5 million people, how many would you expect to have the disease?

Ratio and Proportion:

A ratio is a comparison of two numbers. To compare ratios, write them as fractions. Proportion can be denoted in two ways: using a colon, {eq}a:b =c:d {/eq} or using fraction, {eq}\dfrac{a}{b}=\dfrac{c}{d} {/eq}. It is a statement that two ratios are equal.

Answer and Explanation: 1

In a population of 10,000 people, 9 were affected to a certain disease. From this we have:

$$\frac{9}{10,000} $$

The expected number of people that will catch the disease will be represented by a variable {eq}n{/eq} in a place with 4,500,000 population.

$$\frac{n}{4,500,000} $$

Now, create a ratio and proportion using the fraction method.

$$\frac{9}{10,000}=\frac{n}{4,500,000} $$

Simplify to solve for {eq}n{/eq}:

$$\begin{align} n(10,0000) &= (4,500,000) (9) \\[0.3cm] n (10,000) &= (40,500,000) \\[0.3cm] \frac{n(10,000)}{10,000} &= \frac{40,500,000}{10,000} \\[0.3cm] n &= 4,050 \end{align} \\ $$

Therefore, in a city with 4,500,000 population, {eq}\boxed{4,050} {/eq} people are expected to catch a certain disease.


Learn more about this topic:

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Practice Problems for Calculating Ratios and Proportions

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Chapter 30 / Lesson 3
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In this lesson, you'll get a quick review of a type of math problem that shows up on the SAT: ratios and proportions. We'll walk through some problems in the video, and you can test your skills in the quiz questions.


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