Step by step
The question
Question: The mean of 5 quiz scores is 88.
What score on the next quiz makes the mean 89?
1 Total needed
After the next quiz there will be 6 scores.
For a mean of 89, the 6 scores must add up to 89 times 6.
That is 534.
total needed = 89 × 6 = 534
The mean times how many numbers gives the total.
That is the key idea today.
mean × how many = total
Careful!
With the next quiz, there are 6 scores, not 5.
So we multiply by 6.
Careful: not 89 × 5 ✗
2 Total so far
5 scores with a mean of 88 add up to 88 times 5.
That is 440.
total so far = 88 × 5 = 440
3 What is missing
The total must go from 440 up to 534.
The missing part is 534 minus 440.
That is 94.
next quiz = 534 − 440 = 94
4 Check
Let's check: 440 plus 94 is 534.
And 534 divided by 6 is 89, the mean we wanted.
So it is right!
440 + 94 = 534, 534 ÷ 6 = 89
Let's look back.
First: total needed.
Then: total so far.
Then: what is missing.
Last: check.
Answer
next quiz = 534 − 440 = 94