SOLUTION: a fraction becomes 5/6 if 3 is added to both the numerator and denominator.if however 3 is subtracted from both numerator and denominator the fraction becomes 2/3 find the fraction

Question 744340: a fraction becomes 5/6 if 3 is added to both the numerator and denominator.if however 3 is subtracted from both numerator and denominator the fraction becomes 2/3 find the fraction
Answer by checkley79(3341) (Show Source): You can put this solution on YOUR website!
(X+3)/(Y+3)=5/6
6(X+3)=5(Y+3)
6X+18=5Y+15
6X-5Y=15-16
6X-5Y=-1
(X-3)/(Y-3)=2/3
3(X-3)=2(Y-3)
3X-9=2Y-6
3X-2Y=-6+9
#######################
3X-2Y=3 MULTIPLY BY -2 & ADD.
6X-5Y=-1
-6X+4Y=-6
--------------
-Y=-7
Y=7 ANS.
6X-5*7=-1
6X-35=-1
6X=35-1
6X=34
X=34/6
X=5 2/3 ANS.
PROOF:
3(5 2/3)-2*7=3
3(17/3)-14=3
17-14=3
3=3
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