Question

To get onto the Honor Roll, Max has to get an average in math of at least a 90.

For five exams, he has an average of 88. What must he score on the next exam
to bring his average up to exactly 90?

Answer 1

He needs to score 100 in his next test.

Explanation:

The average of the exams is given by the sum of each exam score divided by the number of exams he took, therefore his prior average is:

`\text{prior average} = \frac{\text{prior sum of grades}}{\text{prior number of tests}}`

Since he took five exams and had an average of 88, then his prior sum of grades is:

`\text{prior sum of grades} = 88*5 = 440`

He needs to score "x" in his next test in order to have an 90 average, therefore if we add "x" to the sum of his grades and add 1 to the prior number of tests then equal that to 90, we can solve for "x". We have:

`\text{desired average} = \frac{\text{prior sum of grades} + x}{\text{prior number of texts}+1}\\90 = (440 +x)/(6)\\440 + x = 90*6\\x = 540 - 440\\x = 100\\`

He needs to score 100 in his next test.