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

1/8x + 1/2y = 52

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

48
52
80
96

Answer 1

The answer you get is (96,80). 96 is greater.

Answer 2

Answer : 96

x – y = 16 --------> equation 1

`(1)/(8) x +(1)/(2) y = 52`

x is the higher grade and y is the lower grade

We solve the first equation for y

x - y = 16

-y = 16 -x ( divide each term by -1)

y = -16 + x

Now substitute y in second equation

`(1)/(8) x +(1)/(2) ( -16 + x ) = 52`

`(1)/(8) x - 8 + (1)/(2) x = 52`

`(1)/(8) x + (1)/(2) x - 8 = 52`

Take common denominator to combine fractions

`(1)/(8) x + (4)/(8) x -8 = 52`

`(5)/(8) x - 8 = 52`

Add 8 on both sides

`(5)/(8) x = 60`

Multiply both sides by
`(8)/(5)`

x = 96

We know x is the higher grade

96 is the higher grade of Jose’s two tests.