Question

Anna 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, 382 people went to The Youth Wing, 461 people went to Social Issues, and 355 went to Fiction and Literature. On Sunday, the library had 800 total visitors. Based on what Anna had recorded on Saturday, about how many people should be expected to go to The Youth Wing? Round your answer to the nearest whole number.

Answer 1

Based on the data recorded by Anna on Saturday, we can estimate the number of people expected to visit The Youth Wing on Sunday.

Let's calculate the proportion of visitors to The Youth Wing compared to the total number of visitors on Saturday:

`\displaystyle \text{Proportion} = \frac{\text{Visitors to The Youth Wing on Saturday}}{\text{Total visitors on Saturday}} = (382)/(382 + 461 + 355)`

Next, we'll apply this proportion to the total number of visitors on Sunday to estimate the number of people expected to go to The Youth Wing:

`\displaystyle \text{Expected visitors to The Youth Wing on Sunday} = \text{Proportion} * \text{Total visitors on Sunday}`

Now, let's substitute the values into the equation and calculate the estimated number of visitors to The Youth Wing on Sunday:

`\displaystyle \text{Proportion} = (382)/(382 + 461 + 355)`

`\displaystyle \text{Expected visitors to The Youth Wing on Sunday} = \text{Proportion} * 800`

Calculating the proportion:

`\displaystyle \text{Proportion} = (382)/(382 + 461 + 355) = (382)/(1198)`

Calculating the estimated number of visitors to The Youth Wing on Sunday:

`\displaystyle \text{Expected visitors to The Youth Wing on Sunday} = (382)/(1198) * 800`

Simplifying the equation:

`\displaystyle \text{Expected visitors to The Youth Wing on Sunday} \approx (382 * 800)/(1198)`

Now, let's calculate the approximate number of visitors to The Youth Wing on Sunday:

`\displaystyle \text{Expected visitors to The Youth Wing on Sunday} \approx 254`

Therefore, based on the data recorded on Saturday, we can estimate that around 254 people should be expected to go to The Youth Wing on Sunday.

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