Chapter 12.8, Problem 44E

To determine

To select: the correct option that gives the value of $\frac{H}{L}$ .

Answer to Problem 44E

D

Explanation of Solution

Given information:

The high and low score is denoted by $H\text{ and }L$ respectively.

  $H-L=\frac{H+L}{2}$

The options are shown below.

1. $\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$
2. 2
3. $\raisebox{1ex}{$5$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$
4. 3
5. It cannot be determined from the information given.

Calculation:

Simplify the equation as follows:

  $\begin{array}{c}H-L=\frac{H+L}{2}\\ \frac{H}{L}-1=\frac{H}{2L}+\frac{1}{2}\left[\text{Divide both sides by }L\right]\\ \frac{H}{L}-\frac{H}{2L}=\frac{1}{2}+1\\ \frac{2H-H}{2L}=\frac{1+2}{2}\\ \frac{H}{2L}=\frac{3}{2}\\ \frac{H}{L}=3\end{array}$

Since the value is 3, thus option D is correct.