jose asks his friends to guess the higher of two grades he received on his math tests. he gives them two…
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.\n$x - y = 16$\n$\frac{1}{8}x+\frac{1}{2}y = 52$\nwhat is the higher grade of joses two tests?\n48\n52\n80\n96
Answer
Explanation:
Step1: Express y in terms of x
From $x - y=16$, we get $y=x - 16$.
Step2: Substitute y into the second - equation
Substitute $y=x - 16$ into $\frac{1}{8}x+\frac{1}{2}y = 52$. We have $\frac{1}{8}x+\frac{1}{2}(x - 16)=52$. Expand the equation: $\frac{1}{8}x+\frac{1}{2}x-8 = 52$. Combine like - terms: $\frac{1 + 4}{8}x-8 = 52$, so $\frac{5}{8}x-8 = 52$.
Step3: Solve for x
Add 8 to both sides of the equation: $\frac{5}{8}x=52 + 8=60$. Multiply both sides by $\frac{8}{5}$: $x=60\times\frac{8}{5}=96$.
Answer:
96