SOLUTION: If the numerator and denominator of a fraction are each increased by 1, the result is 35; but if the numerator and denominator are each decreased by 1, the result is 59. Let the f

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: If the numerator and denominator of a fraction are each increased by 1, the result is 35; but if the numerator and denominator are each decreased by 1, the result is 59. Let the f      Log On


   

Question 722984: If the numerator and denominator of a fraction are each increased by 1, the result is 35; but if the numerator and denominator are each decreased by 1, the result is 59.
Let the fraction be ab. Write down two equations satisfied by a and b:
(i)
(ii)
Find the fraction. ab
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39838) About Me  (Show Source):
You can put this solution on YOUR website!
Your assignment instruction for ab seems strange. Let me try n/d instead.

%28n%2B1%29%2F%28d%2B1%29=35 and %28n-1%29%2F%28d-1%29=59.

The +1 equation gives
n+1=35(d+1)
n+1=35d+35
n-35d=34.

The -1 equation gives
n-1=59(d-1)
n-1=59d-59
n-59d=-60

Subtracting the -60 equation from the +34 equation gives us:
(59-34)d=94
25d=94
d=3.76 and using in the +1 equation result gives n=165.6

Your fraction, as n/d, should be 165.6%2F3.76=44.0425532

Answer by MathTherapy(10858) About Me  (Show Source):
You can put this solution on YOUR website!

If the numerator and denominator of a fraction are each increased by 1, the result is 35; but if the numerator and denominator are each decreased by 1, the result is 59.
Let the fraction be ab. Write down two equations satisfied by a and b:
(i)
(ii)
Find the fraction. ab

%28a+%2B+1%29%2F%28b+%2B+1%29+=+35 ---- 35b + 35 = a + 1 ----- a – 35b = 34 ---- eq (i)

%28a+-+1%29%2F%28b+-+1%29+=+59 ---- 59b – 59 = a – 1 ----- a – 59b = - 58 ---- eq (ii)

Solving, a = highlight_green%28168.1667%29, and b = highlight_green%283.833333%29

You can do the check!!

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