Emily volunteers on the weekend at the Central Library. As a school project, she decides to record how many people visit the library, and where they go. On Saturday, $416$ people went to The Youth Wing, $448$ people went to Social Issues, and $341$ went to Fiction and Literature. $\newline$ On Sunday, the library had $500$ total visitors. Based on what Emily had recorded on Saturday, about how many people should be expected to go to Social Issues? Round your answer to the nearest whole number.

View step-by-step help

Home

Math Problems

Algebra 2

Find probabilities using combinations and permutations

Full solution

Q. Emily volunteers on the weekend at the Central Library. As a school project, she decides to record how many people visit the library, and where they go. On Saturday,

416

people went to The Youth Wing,

448

people went to Social Issues, and

341

went to Fiction and Literature.

\newline

On Sunday, the library had

500

total visitors. Based on what Emily had recorded on Saturday, about how many people should be expected to go to Social Issues? Round your answer to the nearest whole number.

Find Total Visitors: First, let's find the total number of visitors on Saturday to get a sense of the distribution across the different sections.
Calculate Proportion: Add the number of people who went to The Youth Wing, Social Issues, and Fiction and Literature on Saturday. $416$ (Youth Wing) + $448$ (Social Issues) + $341$ (Fiction and Literature) = $1205$ total visitors on Saturday.
Estimate Visitors: Next, let's calculate the proportion of visitors that went to Social Issues on Saturday.
Round to Nearest Whole: Divide the number of visitors to Social Issues by the total number of visitors on Saturday. $\newline$ $448$ (Social Issues) / $1205$ (Total Visitors) $\approx 0.3718$
Round to Nearest Whole: Divide the number of visitors to Social Issues by the total number of visitors on Saturday. $\newline$ $448$ (Social Issues) / $1205$ (Total Visitors) $\approx 0.3718$ Now, let's use this proportion to estimate the number of visitors to Social Issues on Sunday.
Round to Nearest Whole: Divide the number of visitors to Social Issues by the total number of visitors on Saturday. $\newline$ $\frac{448 \text{ (Social Issues)}}{1205 \text{ (Total Visitors)}} \approx 0.3718$ Now, let's use this proportion to estimate the number of visitors to Social Issues on Sunday.Multiply the total number of visitors on Sunday by the proportion that went to Social Issues on Saturday. $\newline$ $500 \text{ (Total Visitors on Sunday)} \times 0.3718 \text{ (Proportion for Social Issues)} \approx 185.9$
Round to Nearest Whole: Divide the number of visitors to Social Issues by the total number of visitors on Saturday. $\newline$ $448$ (Social Issues) / $1205$ (Total Visitors) $\approx 0.3718$ Now, let's use this proportion to estimate the number of visitors to Social Issues on Sunday.Multiply the total number of visitors on Sunday by the proportion that went to Social Issues on Saturday. $\newline$ $500$ (Total Visitors on Sunday) * $0.3718$ (Proportion for Social Issues) $\approx 185.9$ Round the result to the nearest whole number to get the expected number of visitors to Social Issues on Sunday.