Math Test Score

Question

In a recent math test, Carmen's score was recorded incorrectly by the teacher. Her real score was exactly five times the score the teacher recorded. When the score was fixed, the average score for the entire class increased by two points out of 100. If there are 26 students in the class (including Carmen), what was Carmen's real score on the test?

Answer 1

If we call Carmen's wrong score W, and her real score R,

then R = 5W

Let's call the original mean average score for the class, A.

That means there were 26 * A points scored by the 26 students.

Let's set N = New Average. N = A + 2.

That means there are 26 * N, or 26 (A + 2) points scored now.

This multiplies out to 26A + 52 points total scored by the class, as opposed to the original of 26A.

Carmen's new score is 5 times bigger than her original score, and this difference accounts for 52 points.

Since R = 5W, then R - W = 5W - W, or 4W. 4W = 52, so W = 13.

R = 5W = 5(13), or 85.

There's probably a simpler way of explaining this, but this is how it flowed out as I was working on it.