Ravi's test scores are 78, 84, 81 and 85. What score on the next… Step by Step

Step by step

The question

Question: Ravi's test scores are 78, 84, 81 and 85.

What score on the next test makes his mean 83?

There are four choices.

First we solve it, the normal way.

Then we pick.

1 Total needed

After the next test there will be 5 scores.

For a mean of 83, the 5 scores must add up to 83 times 5.

That is 415.

total needed = 83 × 5 = 415

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 5 scores, not 4.

So we multiply by 5.

Careful: not 83 × 4 ✗

2 Total so far

Now we add the 4 scores we know, from left to right.

total so far = 78 + 84 + 81 + 85

So far, the total is 328.

total so far = 328

3 What is missing

The total must go from 328 up to 415.

The missing part is 415 minus 328.

That is 87.

next test = 415 − 328 = 87

4 Check

Let's check: 328 plus 87 is 415.

And 415 divided by 5 is 83, the mean we wanted.

So it is right!

328 + 87 = 415, 415 ÷ 5 = 83

5 Pick the choice

Our answer is 87.

That is choice D.

D) 87

6 Why not the others

A is 4.

Wrong: 83 × 4: after the next test there are 5 scores, not 4.

A) 4 ✗ 83 × 4: after the next test there are 5 scores, not 4

B is 83.

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

B) 83 ✗ that is the mean we want, not the score that makes it

C is 84.

Wrong: 83 + 1: each of the 4 scores is 1 below 83, so the next one must make up 4.

C) 84 ✗ 83 + 1: each of the 4 scores is 1 below 83, so the next one must make up 4

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