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 shown.
$x - y = 16$
$\frac{1}{8}x+\frac{1}{2}y = 52$
what is the higher grade of joses two tests?
80
96
48
52

Explanation:

Step1: Express \( y \) from first equation

From \( x - y = 16 \), we get \( y = x - 16 \).

Step2: Substitute \( y \) into second equation

Substitute \( y = x - 16 \) into \( \frac{1}{8}x + \frac{1}{2}y = 52 \):
\[
\frac{1}{8}x + \frac{1}{2}(x - 16) = 52
\]

Step3: Simplify the equation

Expand and simplify:
\[
\frac{1}{8}x + \frac{1}{2}x - 8 = 52
\]
Combine like terms:
\[
\frac{1}{8}x + \frac{4}{8}x = 52 + 8
\]
\[
\frac{5}{8}x = 60
\]

Step4: Solve for \( x \)

Multiply both sides by \( \frac{8}{5} \):
\[
x = 60 \times \frac{8}{5} = 96
\]

Answer:

96