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Archy [21]
3 years ago
8

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 StartFraction 1 over 8 EndFraction x plus StartFraction one-half EndFraction y equals 52.x + StartFraction one-half EndFraction x plus StartFraction one-half EndFraction y equals 18.y = 52 What is the higher grade of Jose’s two tests?
Mathematics
1 answer:
tatyana61 [14]3 years ago
8 0

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.

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