Step by step
The question
Question: Ben's game points are 60, 74, 68 and 70.
What number of points in the next game makes his mean 70?
1 Total needed
After the next game there will be 5 points.
For a mean of 70, the 5 points must add up to 70 times 5.
That is 350.
total needed = 70 × 5 = 350
The mean times how many numbers gives the total.
That is the key idea today.
mean × how many = total
Careful!
With the next game, there are 5 points, not 4.
So we multiply by 5.
Careful: not 70 × 4 ✗
2 Total so far
Now we add the 4 points we know, from left to right.
total so far = 60 + 74 + 68 + 70
So far, the total is 272.
total so far = 272
3 What is missing
The total must go from 272 up to 350.
The missing part is 350 minus 272.
That is 78.
next game = 350 − 272 = 78
4 Check
Let's check: 272 plus 78 is 350.
And 350 divided by 5 is 70, the mean we wanted.
So it is right!
272 + 78 = 350, 350 ÷ 5 = 70
Let's look back.
First: total needed.
Then: total so far.
Then: what is missing.
Last: check.
Answer
next game = 350 − 272 = 78