Question

On his first 4 tests Eric scored a 93,92,85,82. What will he have to score on his last test to average a 90? Make a variable equation and a solution

Answer 1

• (93+92+85+82+s)/5 = 90
• s = 98
• Eric will have to score 98 on his last test to average 90

Explanation:

The average is the sum of scores divided by the number of them. The total number of scores, including score "s" on his last test is 5. So, the average is the total divided by 5:

(93+92+85+82+s)/5 = 90

The solution to this is ...

352 +s = 450 . . . multiply by 5

s = 98 . . . . . . . . . . subtract 352

Eric must score 98 on his last test.

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Alternate Solution

I like to work problems like this by considering the differences from average. Here's the long justification for doing that.

(93+92+85+82+s)/5 = 90

93 +92 +85 +82 +s = 90 +90 +90 +90 +90 . . . . . multiply by 5

(93 -90) +(92 -90) +(85 -90) +(82 -90) +s = 90 . . . . subtract 360

3 +2 -5 -8 +s = 90 . . . . compute the differences from average

-8 +s = 90 . . . . . . . . . . . add them up

s = 90 +8 = 98 . . . . . . . add their opposite to the average (This makes the total of all differences from average be zero, as it must be.)

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The short expression of this method is ...

s = (average) + (–(sum of differences from average))