Question

ch 7 test retake
do not write on the test

1. bryan had grades of 85, 92, 98, 96, and 89 on his last five math tests. what grade does he need on his next test to have an average of 91?

a. 98
b. 95
c. 91
d. 86

Explanation:

Step1: Recall the average formula

The formula for the average of \( n \) numbers is \( \text{Average} = \frac{\text{Sum of numbers}}{n} \). Here, after the next test, there will be \( 6 \) tests, and we want the average to be \( 91 \). So the total sum of all \( 6 \) tests should be \( 91\times6 \).

Step2: Calculate the sum of the first five tests

The grades of the first five tests are \( 85, 92, 98, 96, 89 \). Let's find their sum: \( 85 + 92 + 98 + 96 + 89 \).
First, \( 85+92 = 177 \), \( 177+98 = 275 \), \( 275+96 = 371 \), \( 371+89 = 460 \).

Step3: Let \( x \) be the grade on the next test

We know that the sum of six tests is \( 460 + x \), and this should equal \( 91\times6 \). Calculate \( 91\times6 = 546 \). So we have the equation \( 460 + x = 546 \).

Step4: Solve for \( x \)

Subtract \( 460 \) from both sides of the equation: \( x = 546 - 460 \). \( 546 - 460 = 86 \).

Answer:

d. 86