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
1/8x - 8 + 1/2 x = 52
1/8x + 1/2x - 8 = 52
Take common denominator to combine fractions
1/8x + 4/8x -8 = 52
5/8x - 8 = 52
Add 8 on both sides
5/8x = 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.
The higher grade and lower grade of Jose’s two tests will be 96 and 80.
The solution of the equation means the value of the unknown or variable.
Jose asks his friends to guess the higher of two grades he received on his math tests.
He gives them two hints.
Let x be the higher number and y be the lower number.
The difference of the two grades is 16.
x - y = 16 ...1
The sum of one-eighth of the higher grade and one-half of the lower grade is 52.
x/8 + y/2 = 52
x + 4y = 416 ...2
Subtract equation 1 from 2, we have
4y + y = 416 – 16
5y = 400
y = 80
Then the value of x will be
x – 80 = 16
x = 80 + 16
x = 96
The higher grade and lower grade of Jose’s two tests will be 96 and 80.
More about the solution of the equation link is given below.
https://brainly.com/question/545403
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