Chapter A.9, Problem 119AYU

To determine

To find:

a. Solve an inequality to find the range of the score that you need on the last test to get a B.

b. What score do you need if the fifth test counts double?

Answer to Problem 119AYU

a. If you get at least 74 you can get score a grade of B

b. If you get at least 37 you can get score a grade of B

Explanation of Solution

Given:

You have scores of 68, 82, 87, and 89 on the first four of five tests. To get a grade of B, the average of the first five test scores must be greater than or equal to 80 and less than 90.

Calculation:

$\text{Total of first four test} = 68 + 82 + 87 + 89 = 326$

If average score is 80 to 90

$\begin{array}{l}80 \le \frac{326 + x}{5} \le 90\\ 400 \le 326 + x \le 450\\ 74 \le x \le 124\end{array}$

Since it is impossible to make over 100

$74 \le x \le 100$

If you get at least 74 you can get score a grade of B

If the fifth test count double

$\begin{array}{l}80 \le \frac{326 + 2x}{5} \le 90\\ 400 \le 326 + 2x \le 450\\ 74 \le 2x \le 124\\ 37 \le x \le 62\end{array}$

If you get at least 37 you can get score a grade of B