Step by step
The question
Question: The mean of 3 test scores is 90.
What score on the next test makes the mean 88?
1 Total needed
After the next test there will be 4 scores.
For a mean of 88, the 4 scores must add up to 88 times 4.
That is 352.
total needed = 88 × 4 = 352
The mean times how many numbers gives the total.
That is the key idea today.
mean × how many = total
Careful!
With the next test, there are 4 scores, not 3.
So we multiply by 4.
Careful: not 88 × 3 ✗
2 Total so far
3 scores with a mean of 90 add up to 90 times 3.
That is 270.
total so far = 90 × 3 = 270
3 What is missing
The total must go from 270 up to 352.
The missing part is 352 minus 270.
That is 82.
next test = 352 − 270 = 82
4 Check
Let's check: 270 plus 82 is 352.
And 352 divided by 4 is 88, the mean we wanted.
So it is right!
270 + 82 = 352, 352 ÷ 4 = 88
Let's look back.
First: total needed.
Then: total so far.
Then: what is missing.
Last: check.
Answer
next test = 352 − 270 = 82