Step by step
The question
Question: Leo's test scores are 70, 82, 76 and 80.
What score on the next test makes his mean 78?
1 Total needed
After the next test there will be 5 scores.
For a mean of 78, the 5 scores must add up to 78 times 5.
That is 390.
total needed = 78 × 5 = 390
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 78 × 4 ✗
2 Total so far
Now we add the 4 scores we know, from left to right.
total so far = 70 + 82 + 76 + 80
So far, the total is 308.
total so far = 308
3 What is missing
The total must go from 308 up to 390.
The missing part is 390 minus 308.
That is 82.
next test = 390 − 308 = 82
4 Check
Let's check: 308 plus 82 is 390.
And 390 divided by 5 is 78, the mean we wanted.
So it is right!
308 + 82 = 390, 390 ÷ 5 = 78
Let's look back.
First: total needed.
Then: total so far.
Then: what is missing.
Last: check.
Answer
next test = 390 − 308 = 82