A local library manager randomly surveys 80 patrons about the type of book they borrow when they visit the library. The manager finds that 3 patrons borrow novels. If the local library has 345 patrons, approximately how many of them borrow novels when they visit the library? Round your answer to the nearest whole number. (1 point)

Question

______ patrons

Answer 1

To find the estimated number of patrons that borrow novels, you can set up a proportion based on the data from the survey.

From the survey:

• 3 out of 80 patrons borrow novels.

We can represent this as: \[ \frac{3}{80} \]

To find the estimated number of patrons who borrow novels in the entire library, which has 345 patrons, we set up the equation: \[ \frac{3}{80} = \frac{x}{345} \]

Where \( x \) is the estimated number of patrons borrowing novels. Cross-multiplying gives: \[ 3 \times 345 = 80 \times x \]

Calculating \( 3 \times 345 \): \[ 3 \times 345 = 1035 \]

Now, we have: \[ 1035 = 80x \]

To find \( x \), divide both sides by 80: \[ x = \frac{1035}{80} \]

Calculating \( \frac{1035}{80} \): \[ x = 12.9375 \]

Rounding to the nearest whole number: \[ x \approx 13 \]

Thus, the estimated number of patrons who borrow novels when they visit the library is: \[ \boxed{13} \]