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Ronald Fast Food randomly selected $20\%$ of locations and asked the manager about the most popular meat. Of the locations surveyed, beef is the most popular meat at $4$ locations. Based on the data, what is the most reasonable estimate of the number of Ronald Fast Food locations where the most popular meat is beef?

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Estimate population size using proportions

Full solution

Q. Ronald Fast Food randomly selected

20\%

of locations and asked the manager about the most popular meat. Of the locations surveyed, beef is the most popular meat at

4

locations. Based on the data, what is the most reasonable estimate of the number of Ronald Fast Food locations where the most popular meat is beef?

Understand Given Information: Understand the given information and what is being asked. $\newline$ We know that $20\%$ of the locations were surveyed, and at $4$ of those locations, beef is the most popular meat. We need to estimate the total number of locations where beef is the most popular meat.
Set Up Proportion: Set up the proportion to find the total number of locations. $\newline$ If $4$ locations represent $20\%$ of the total locations, we can set up a proportion where $4$ is to $20\%$ as the total number of locations where beef is popular (let's call this number $x$ ) is to $100\%$ . $\newline$ $\frac{4}{20\%} = \frac{x}{100\%}$
Solve for x: Solve the proportion for $x$ . $\newline$ Cross-multiply to solve for $x$ . $\newline$ $4 \times 100\% = x \times 20\%$ $\newline$ $400\% = 20x$
Isolate $x$ : Divide both sides by $20$ to isolate $x$ . $\frac{400\%}{20} = \frac{20x}{20}$ $20 = x$

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