Step by step
The question
Question: The mean of 3 numbers is 15.
Two of them are 11 and 19.
What is the third number?
1 Total needed
There are 3 numbers with a mean of 15.
So all 3 add up to 15 times 3.
That is 45.
total needed = 15 × 3 = 45
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 3 numbers, not just the 2 we know.
So we multiply by 3.
Careful: not 15 × 2 ✗
2 Total so far
Now we add the 2 numbers we know, from left to right.
total so far = 11 + 19
So far, the total is 30.
total so far = 30
3 What is missing
The total must go from 30 up to 45.
The missing part is 45 minus 30.
That is 15.
third number = 45 − 30 = 15
4 Check
Let's check: 30 plus 15 is 45.
And 45 divided by 3 is 15, the mean we wanted.
So it is right!
30 + 15 = 45, 45 ÷ 3 = 15
Let's look back.
First: total needed.
Then: total so far.
Then: what is missing.
Last: check.
Answer
third number = 45 − 30 = 15