The mean of 6 test scores is 80. What score on the next test makes… Step by Step

Step by step

The question

Question: The mean of 6 test scores is 80.

What score on the next test makes the mean 82?

There are four choices.

First we solve it, the normal way.

Then we pick.

1 Total needed

After the next test there will be 7 scores.

For a mean of 82, the 7 scores must add up to 82 times 7.

That is 574.

total needed = 82 × 7 = 574

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 7 scores, not 6.

So we multiply by 7.

Careful: not 82 × 6 ✗

2 Total so far

6 scores with a mean of 80 add up to 80 times 6.

That is 480.

total so far = 80 × 6 = 480

3 What is missing

The total must go from 480 up to 574.

The missing part is 574 minus 480.

That is 94.

next test = 574 − 480 = 94

4 Check

Let's check: 480 plus 94 is 574.

And 574 divided by 7 is 82, the mean we wanted.

So it is right!

480 + 94 = 574, 574 ÷ 7 = 82

5 Pick the choice

Our answer is 94.

That is choice D.

D) 94

6 Why not the others

A is 12.

Wrong: 82 × 6: after the next test there are 7 scores, not 6.

A) 12 ✗ 82 × 6: after the next test there are 7 scores, not 6

B is 82.

Wrong: that is the mean we want, not the score that makes it.

B) 82 ✗ that is the mean we want, not the score that makes it

C is 84.

Wrong: 82 + 2: each of the 6 scores is 2 below 82, so the next one must make up 12.

C) 84 ✗ 82 + 2: each of the 6 scores is 2 below 82, so the next one must make up 12

Let's look back.

First: total needed.

Then: total so far.

Then: what is missing.

Then: check.

Then: pick the choice.

Last: why not the others.

Answer