SOLUTION: If 7/8 is decreased by the reciprocal of a number, the result is 39/8. Find the number

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Question 1178443: If 7/8 is decreased by the reciprocal of a number, the result is 39/8. Find the number
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

let a number be x, and its reciprocal 1%2Fx
If 7%2F8 is decreased by the reciprocal of a number, the result is 39%2F8, so we have
7%2F8-1%2Fx=39%2F8
7%2F8-39%2F8=+1%2Fx
-32%2F8=+1%2Fx
x=-8%2F32
x=-1%2F4 ->the number

check:
the reciprocal of a number -1%2F4 is -4

7%2F8-%28-4%29=39%2F8
7%2F8%2B4=39%2F8
7%2F8%2B32%2F8=39%2F8
39%2F8=39%2F8