Chapter 8.8, Problem 62STP

To determine

Find the correct choice from the given options.

Answer to Problem 62STP

Option D is correct.

Explanation of Solution

Given:

Sandra`s scores on the first five science tests are shown. Which inequality represents the score she must receive on the sixth test to have an average score more than 88?

Test	1	2	3	4	5
Score	85	84	90	95	88

Options are: $\text{A: s }\ge \text{ 86; B: s }\le \text{ 88; C: s < 88; D: s > 86 }$

Concept Used:

Let x represents the score for the sixth test.

Average = $\frac{\text{Total score of all tests }}{\text{Number}\text{of}\text{tests}}$

Here number of tests = 6 and total of six tests is: $85\text{ + 84 + 90 + 95 +88 + x = 442 +x }$

Calculation:

Average = $\frac{\text{Total score of all tests }}{\text{Number}\text{of}\text{tests}}$

Here number of tests = 6 and total of six tests is: $85\text{ + 84 + 90 + 95 +88 + x = 442 +x }$

According to the question the average scores more than 88.

The required inequality: $\frac{442+x}{6}\text{ > 88}$

Solve for x: $\begin{array}{l}6·\frac{442+x}{6}\text{ > }6·\text{88}\\ \text{442}\text{+}\text{x}\text{>}\text{528}\text{[ Multiply each side by 6 ] }\\ \text{442}\text{-}\text{442}\text{+}\text{x}\text{>}\text{528}\text{-}\text{442}\text{[ Subtract both sides by 442 ]}\\ \text{x > 86 }\end{array}$

Sandra must receive more than 86 on the sixth test to have an average score more than 88.

Option D is correct.

Thus, option D is correct.