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Firlakuza [10]
3 years ago
12

Jose asks his friends to guess the higher of two grades he received on his math tests. He gives them two hints. The difference o

f 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
Mathematics
2 answers:
AlekseyPX3 years ago
6 0

Answer : 96

x – y = 16 --------> equation 1

\frac{1}{8} x +\frac{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

\frac{1}{8} x +\frac{1}{2} ( -16 + x ) = 52

\frac{1}{8} x - 8 +   \frac{1}{2} x = 52

\frac{1}{8} x  +   \frac{1}{2} x - 8 = 52

Take common denominator to combine fractions

\frac{1}{8} x  +   \frac{4}{8} x  -8 = 52

\frac{5}{8} x - 8  = 52

Add 8 on both sides

\frac{5}{8} x   = 60

Multiply both sides by \frac{8}{5}

x = 96

We know x is the higher grade

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

svetlana [45]3 years ago
6 0
The answer you get is (96,80). 96 is greater.
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