Question

Jose asks his friends to guess the higher of two grades he received on his math tests. He gives them two hints. The difference of the two grades is 16. The sum of one-eighth of the higher grade and one-half of the lower grade is 52. The system that represents his scores is below.

x – y = 16

x + y = 52

What is the higher grade of Jose’s two tests?

48
52
80
96

Answer 1

I'm a bit confused as to whether the second equation in the system of linear equations is correct or not. It's stated in the question as being x + y = 52, but the question also says that:
"The sum of one-eighth of the higher grade and one-half of the lower grade is 52."

Surely that means, given that we are taking x to be the higher grade and y to be the lower grade, that the correct equation would be:
\[\frac{ 1 }{ 8 }x + \frac{ 1 }{ 2 }y = 52\]

Answer 2

80