Step by step
The question
Question: The mean of 4 test scores is 82.
What score on the next test makes the mean 84?
1 Total needed
After the next test there will be 5 scores.
For a mean of 84, the 5 scores must add up to 84 times 5.
That is 420.
total needed = 84 × 5 = 420
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 5 scores, not 4.
So we multiply by 5.
Careful: not 84 × 4 ✗
2 Total so far
4 scores with a mean of 82 add up to 82 times 4.
That is 328.
total so far = 82 × 4 = 328
3 What is missing
The total must go from 328 up to 420.
The missing part is 420 minus 328.
That is 92.
next test = 420 − 328 = 92
4 Check
Let's check: 328 plus 92 is 420.
And 420 divided by 5 is 84, the mean we wanted.
So it is right!
328 + 92 = 420, 420 ÷ 5 = 84
Let's look back.
First: total needed.
Then: total so far.
Then: what is missing.
Last: check.
Answer
next test = 420 − 328 = 92