#### Question

Andrews and Associates specialize in corporate law. They charge $100 an hour for researching a case,$75 an hour for consultations, and \$200 an hour for writing a brief. Last week one of the associates spent 10 hours consulting with her client, 10 hours researching the case, and 20 hours writing the brief. What was the weighted mean hourly charge for her legal services?

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#### Step 1

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Let $X$ be the hourly charges for the legal services. $X_1$ is for researching a case, $X_2$ is for consultation and $X_3$ is for writing a brief.

$X_1=\100$, $X_2=\75$ and $X_3=\200$.

Let $w$ be the number of hours. $w_1=10$, $w_2=10$ and $w_3=20$.

Weighted mean is $\bar{X}$

\begin{align*} \bar{X}&=\frac{\Sigma wX}{\Sigma w}\\ &=\frac{10 \times 100+10 \times 75+ 20 \times 200}{10+10+20}\\ &=\frac{1000+750+4000}{40}\\ &=\frac{5750}{40}\\ &=143.75 \end{align*}

Weighted mean hourly charge is $\143.75$.

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