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Average Algebra Problem

by Katie
(Indiana )

Here's my problem:

Ahmik's scores on the first four of five 100-point history tests were 85, 91, 89, and 94.

If a grade of at least 90 is an A, write an inequality to find the score Ahmik must receive on the fifth test to have an A test average.

Karin from Algebra Class Says:

In order to solve this problem, we must know how to average a set of numbers. When we average a set of numbers, we must add all of the numbers together and divide by the number of numbers that we added.

The problem here is that we don't know one of the five numbers. However, we do know that when we don't know a value in Algebra, we can assign a variable to the value.

Let's let the missing test score = x.

So, let's perform the arithmetic needed for averages.

(85+91+89+94+x) = 90

This math sentence shows that we will add all of the test scores, including the one that we don't know. We will divide that answer by 5 and get an average of 90 which would be an A grade.

Now we have to solve. (Notice how I put parenthesis around the 5 test scores. Those test scores must stay together and can not be separated.

Our first step is to get rid of the 5 in the denominator. So we will multiply both sides by 5.

5(85+91+89+94+x) = 90(5)

This allows us to get rid of the denominator (the numerator stays the same.)

85+91+89+94+x = 450

Now we can simplify by adding the 85+91+89+94.

359+x = 450

Now solve for x by subtracting 359 from both sides.

359 - 359 +x = 450 -359

x = 91

Therefore, Ahmik needs a score of at least 91 on the last test in order to receive an A average.

Check it: 359+91 = 450 and 450/5 = 90.

Hope this helps.


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