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# Fraction Problem

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614
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If the numerator of a fraction is increased by six, the value of the fraction will increase by one. If the denominator of the original fraction is increased by 36, the value of the original fraction will decrease by one. What is the original fraction?

Dec 27, 2018

#1
+4569
+3

Hint: Try to set up variables, solution will come later.

Dec 27, 2018
#2
+111328
+3

Let the numerator  =  x      and the denominator = y

So.....we have this system

[ x + 6 ] / y   =  [ x / y] + 1

[ x ] / [ y + 36]  =  [ x / y] - 1

Looking at the first equation, we can write

[ x + 6]  /  y  =  [ x + y ] / y          multiply through by y

x + 6     =  x +  y       implies that y = 6

Subbing this into the second equation, we have that

[ x] /  [ 6 + 36]  =  [ x / 6]  - 1

[x ] / 42   =  [ x - 6] / 6         cross-multiply

6x  =  42 [ x - 6]

6x = 42x - 252

-36x = - 252

x = 7

So  the original fraction   is    x / y   =      7 / 6

Dec 27, 2018
edited by CPhill  Dec 27, 2018