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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Grade 7

Estimate population size using proportions

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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?

Identify Given Information: Identify the given information. $\newline$ We have: $\newline$ Percentage of locations surveyed: $20\%$ $\newline$ Number of locations where beef is most popular (from the survey): $4$ $\newline$ We need to find the total number of locations where beef is the most popular meat.
Set Up Proportion: Set up a proportion to represent the relationship between the surveyed locations and the total number of locations. $\newline$ Let $x$ be the total number of locations where beef is the most popular meat. $\newline$ The proportion is based on the idea that the $20\%$ of locations surveyed is representative of the entire set of locations. $\newline$ So, we have: $\newline$ $(\text{Number of surveyed locations where beef is most popular}) / (\text{Total number of surveyed locations}) = (\text{Total number of locations where beef is most popular}) / (\text{Total number of locations})$ $\newline$ $4 / (20\% \text{ of total locations}) = x / (100\% \text{ of total locations})$
Convert Percentage to Fraction: Convert the percentage of locations surveyed into a fraction to use in the proportion. $\newline$ $20\%$ as a fraction is $\frac{20}{100}$ , which simplifies to $\frac{1}{5}$ . $\newline$ So, the proportion becomes: $\newline$ $\frac{4}{\left(\frac{1}{5}\right)\text{ of total locations}} = \frac{x}{\left(1\text{ of total locations}\right)}$
Solve Proportion for $x$ : Solve the proportion for $x$ , the total number of locations where beef is the most popular meat. $\newline$ Cross-multiply to solve for $x$ : $\newline$ $4 \times (1 \text{ of total locations}) = x \times (\frac{1}{5} \text{ of total locations})$ $\newline$ $4 = (\frac{1}{5})x$ $\newline$ Multiply both sides by $5$ to isolate $x$ : $\newline$ $5 \times 4 = x$ $\newline$ $20 = x$