Question

9 fill in the blank 1 point 9. a city wants to build a new park at the weighted average of 2 apartment complexes. one complex located at 24 main st. has 176 units and the other complex at 87 main st. has 124 units. where should the park be built? the park should be located at type your answer... main st. round your answer to the nearest whole number.

Explanation:

Step1: Recall weighted average formula

The weighted average formula for two values \( x_1 \) and \( x_2 \) with weights \( w_1 \) and \( w_2 \) is \( \bar{x}=\frac{w_1x_1 + w_2x_2}{w_1 + w_2} \). Here, \( x_1 = 24 \), \( w_1 = 176 \), \( x_2 = 87 \), \( w_2 = 124 \).

Step2: Calculate numerator

Calculate \( w_1x_1+w_2x_2 = 176\times24 + 124\times87 \).
\( 176\times24 = 4224 \), \( 124\times87 = 10788 \).
Sum: \( 4224 + 10788 = 15012 \).

Step3: Calculate denominator

Calculate \( w_1 + w_2 = 176 + 124 = 300 \).

Step4: Compute weighted average

Divide numerator by denominator: \( \bar{x}=\frac{15012}{300}=50.04 \). Round to nearest whole number: 50.

Answer:

50