Chapter 5.1, Problem 60PFA

To determine

Find the minimum number Marta need to score on her 4^th test to have of 85 or better for all 4 tests.

Answer to Problem 60PFA

Option C is correct.

Explanation of Solution

Given:

Marta scores 85, 70 and 92 on three math tests. What does she need to score on her fourth math test to have an average of 85 or better for all four tests?

There are 4 options:

A: 85 or better; B: better than 93; C: 93 or better; D: 100

Concept Used:

Let Marta score on her 4^th test be x .

Marta scores 85, 70 and 92 on three math tests.

Total score for her in 4 tests = $85+70+92+x$

According to the condition: An average of 85 or better for all four tests.

85 or better means with the sign $\ge$

Average marks = $\frac{\text{Total}\text{Marks}}{\text{No}\text{of}\text{tests}}$ ; Average $\ge$ 85

Inequality: $\frac{85+70+92+x}{\text{4}}\ge 85$

Calculation:

Total score for her in 4 tests = $85+70+92+x$

Average marks = $\frac{\text{Total}\text{Marks}}{\text{No}\text{of}\text{tests}}$ ; Average $\ge$ 85

Inequality: $\frac{85+70+92+x}{\text{4}}\ge 85$

Solve for x :

  $\begin{array}{l}4·\frac{85+70+92+x}{\text{4}}\ge 4·85\ge \text{[}\text{Multiply}\text{both}\text{sides}\text{by}4\text{]}\\ 85+70+92+x\ge 340\\ 85+70+92+x\ge 340\\ 247+x\ge 340\\ 247-247+x\ge 340-247\text{[}\text{Subtract}247\text{from}\text{both}\text{sides}\text{]}\\ x\ge 93\end{array}$

Marta should score 93 or better in the 4^th test.

C: 93 or better is correct.

Thus, Marta should score 93 or better in the 4^th test. Option C is correct.