Chapter 11.1, Problem 35WE

a.

To determine

Verify that Brain was right.

Answer to Problem 35WE

  $Yes$

Explanation of Solution

Given information:

Brian and Lou agreed to equally share the profit from business, Brian and Lou had earned $\$27.50and\$35.50$ profit at end of week, Brian said you owe me half the difference that is $\$4.00$ .

Calculation:

  $\begin{array}{l}Brainprofitattheendofweek,\$27.50\\ Louprofitattheendofweek,\$35.50\\ halfthedifferenceis\$4.00\end{array}]given$

  $\begin{array}{l}27.50+5.00=35.50-4.00\\ 31.50=31.50\end{array}$

Hence, Brain was right.

b.

To determine

Verify that each will have same amount of money.

Answer to Problem 35WE

Both received same amount of money that is $\frac{a+b}{2}$ .

Explanation of Solution

Given information:

Brian and Lou received dollars $aandb$ ,where $b>a$ . If Lou gives Brian $\frac{1}{2}\left(b-a\right)$ dollars.

Calculation:

Given,

Brian recevied $a$ dollars.

Lou recevied $b$ dollars.

If Lou gives Brian $\frac{1}{2}\left(b-a\right)$ dollars,

Calculate Brian recevied money,

  $\begin{array}{l}=a+\frac{1}{2}\left(b-a\right)\\ =a+\frac{b}{2}-\frac{a}{2}\\ =\frac{2a}{2}+\frac{b}{2}-\frac{a}{2}\\ =\frac{a}{2}+\frac{b}{2}\\ =\frac{a+b}{2}\end{array}$

Calculate Lou recevied money,

  $\begin{array}{l}=b-\frac{1}{2}\left(b-a\right)\\ =b-\frac{b}{2}+\frac{a}{2}\\ =\frac{2b}{2}-\frac{b}{2}+\frac{a}{2}\\ =\frac{b}{2}+\frac{a}{2}\\ =\frac{a+b}{2}\end{array}$

Hence, both received same amount of money that is $\frac{a+b}{2}$ .