SOLUTION: in a rational no. twice the numerator is 2 more than the denominator. if 3 is added to each, the numerator or the denominator, the new fraction is 2/3. find the original no.

Question 100024: in a rational no. twice the numerator is 2 more than the denominator. if 3 is added to each, the numerator or the denominator, the new fraction is 2/3. find the original no.
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Let x=the numerator
And let y=the denominator
Now we are told that:
2x=y+2-----------------------eq1
and
(x+3)/(y+3)=2/3-------------------eq2
multiply each term in eq2 by 3(y+3) to get rid of fractions and we get:
3(x+3)=2(y+3) get rid of parens
3x+9=2y+6 subtract 9 from both sides:
3x=2y-3---------------------eq2
multiply eq1 by 2 and subtract it from eq2:
eq2-2*(eq1)=
3x=2y-3
-4x=-2y-4
-x=-7 or
x=7-----------------numerator
substitute x=7 into eq1
2*7=y+2 subtract 2 from both sides
14-2=y
y=12-----------denominator
CK
(7+3)/(12+3)=2/3
10/15=2/3
2/3=2/3
also
2*7=12+2
14=14

Hope this helps-----ptaylor

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