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.
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?
Answers
Given :- 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.
To Find :-
- The system that represents his scores is below.
- what is the higher grade of jose’s two tests ?
Solution :-
Let us assume that, jose grades in test are x and y . where x > y .
then,
→ x - y = 16 ------- Eqn.(1)
and,
→ (x/8) + (y/2) = 52
→ (x + 4y) / 8 = 52
→ x + 4y = 52 * 8
→ x + 4y = 416 ------- Eqn.(2)
Subtracting Eqn.(1) from Eqn.(2) ,
→ (x + 4y) - (x - y) = 416 - 16
→ x - x + 4y + y = 400
→ 5y = 400
→ y = 80
Putting value of y in Eqn.(1)
→ x - 80 = 16
→ x = 16 + 80
→ x = 96.
Hence, the higher grade of jose’s two tests is 96 .
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Answer:
the answer to this question
is D. 96