Sam's first three test scores are 65, 70 and 75. For a mean of 72…

Step by step

The question

Question: Sam's first three test scores are 65, 70 and 75.

For a mean of 72, what score does he need on the next test?

1 Total needed

After the next test there will be 4 scores.

For a mean of 72, the 4 scores must add up to 72 times 4.

That is 288.

The mean times how many numbers gives the total.

That is the key idea today.

Careful!

With the next test, there are 4 scores, not 3.

So we multiply by 4.

2 Total so far

Now we add the 3 scores we know, from left to right.

So far, the total is 210.

3 What is missing

The total must go from 210 up to 288.

The missing part is 288 minus 210.

That is 78.

4 Check

Let's check: 210 plus 78 is 288.

And 288 divided by 4 is 72, the mean we wanted.

So it is right!

Let's look back.

First: total needed.

Then: total so far.

Then: what is missing.

Last: check.