Step by step
The question
Question: The mean of 4 numbers is 9.
Three of them are 7, 12 and 5.
What is the fourth number?
1 Total needed
There are 4 numbers with a mean of 9.
So all 4 add up to 9 times 4.
That is 36.
total needed = 9 × 4 = 36
The mean times how many numbers gives the total.
That is the key idea today.
mean × how many = total
Careful!
The mean is of all 4 numbers, not just the 3 we know.
So we multiply by 4.
Careful: not 9 × 3 ✗
2 Total so far
Now we add the 3 numbers we know, from left to right.
total so far = 7 + 12 + 5
So far, the total is 24.
total so far = 24
3 What is missing
The total must go from 24 up to 36.
The missing part is 36 minus 24.
That is 12.
fourth number = 36 − 24 = 12
4 Check
Let's check: 24 plus 12 is 36.
And 36 divided by 4 is 9, the mean we wanted.
So it is right!
24 + 12 = 36, 36 ÷ 4 = 9
Let's look back.
First: total needed.
Then: total so far.
Then: what is missing.
Last: check.
Answer
fourth number = 36 − 24 = 12