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

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) (Show Source): You can put this solution on YOUR website!
Your assignment instruction for ab seems strange. Let me try n/d instead.

and .

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

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

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

Your fraction, as n/d, should be
Answer by MathTherapy(10858) (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

---- 35b + 35 = a + 1 ----- a � 35b = 34 ---- eq (i)

---- 59b � 59 = a � 1 ----- a � 59b = - 58 ---- eq (ii)

Solving, a = , and b =

You can do the check!!

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