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?

Solution

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Let XX be the hourly charges for the legal services. X1X_1 is for researching a case, X2X_2 is for consultation and X3X_3 is for writing a brief.

X1=$100X_1=\$100, X2=$75X_2=\$75 and X3=$200X_3=\$200.

Let ww be the number of hours. w1=10w_1=10, w2=10w_2=10 and w3=20w_3=20.

Weighted mean is Xˉ\bar{X}

Xˉ=ΣwXΣw=10×100+10×75+20×20010+10+20=1000+750+400040=575040=143.75\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\$143.75.

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