Step by step
The question
Question: The mean of 3 test scores is 75.
For a mean of 78, what score is needed on the next test?
1 Total needed
After the next test there will be 4 scores.
For a mean of 78, the 4 scores must add up to 78 times 4.
That is 312.
total needed = 78 × 4 = 312
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 78 × 3 ✗
2 Total so far
3 scores with a mean of 75 add up to 75 times 3.
That is 225.
total so far = 75 × 3 = 225
3 What is missing
The total must go from 225 up to 312.
The missing part is 312 minus 225.
That is 87.
next test = 312 − 225 = 87
4 Check
Let's check: 225 plus 87 is 312.
And 312 divided by 4 is 78, the mean we wanted.
So it is right!
225 + 87 = 312, 312 ÷ 4 = 78
Let's look back.
First: total needed.
Then: total so far.
Then: what is missing.
Last: check.
Answer
next test = 312 − 225 = 87