ACT Math: Problems Involving Averages

Many of the problems on the ACT Math test — 40% of the problems, in fact — are categorized as Pre-Algebra and Elementary Algebra. These problems test things like averages, ratios, proportions and the like. Often times, students think that because these topics are so basic, they don’t need to review them. But the makers of the ACT find clever ways of testing these seemingly “easy” topics.

Consider the following problem involving averages:

Credit: Fred Kuipers/FreeImages.com
Credit: Fred Kuipers/FreeImages.com

Prof. Walsh teaches two different sections of Physics. In Section 1, there are 40 students, and the class average on a recent test was 84. In Section 2, there are 60 students, and the class average on the same test was 87. What was the average score for all of the students in the two sections on this test?

(A)  85
(B)  85.5
(C)  85.8
(D)  86
(E)  86.2

The “easy” answer to this question would be to average the two class averages, giving you an overall average of (84 + 87) ÷ 2 = 85.5. But that’s not the correct answer!

So how should you approach this problem?

Problems involving averages are often best solved by considering totals. Our work for this problem might look something like this:

Section 1: 40 x 84 = 3360 (total of the scores for Section 1)
Section 2: 60 x 87 = 5220 (total of the scores for Section 2)
Total: 3360 + 5220 = 8580 (total of the scores for all 100 students)
Average: 8580 ÷ 100 = 85.8

The correct answer is Choice (C).

If you want to learn more about Averages and practice some more of these problems, you can go here.

If you have questions about this problem or anything else to do with the ACT, send us an email at info@cardinalec.com

 

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