SOLUTION: can someone help me with this one.. If the numerator and the denominator of a certain fraction are each decreased by 2, the value of the new fraction is 1/2. but if the numerato

Question 511476: can someone help me with this one..
If the numerator and the denominator of a certain fraction are each decreased by 2, the value of the new fraction is 1/2. but if the numerator of the original fraction is increased by 1 and the denominator decreased by 2, the resulting fraction is equal to 3/4. Find the original fraction.
thank you!
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
The original fraction is x/y.
.
We're told:
x-2 / y -2 = 1/2
so
2(x-2) = y-2
2x -4 = y -2
2x -2 = y
so
y = 2x -2
.
We're also told:
x+1 / y-2 = 3/4
so
4x+4 = 3y-6
3y = 4x + 10
y = 4/3x + 10/3
.
Now we have two linear equations and two unknowns.
.
We can graph them see where the intersect.
.

.
Or we can solve the two equations.
.
y = 2x -2
3y = 4x + 10
.
3y = 6x -6
3y = 4x +10
0 = 2x -16
2x = 16
x = 8
.
substitute
.
y = 2(8) -2
y = 14
.
So it appears the first equation is
8/14
.
But always check your answer
.
(x-2)/(y-2) = 6/12 = 1/2
(x+1)/(y-2) = 9/12 = 3/4
.
Answer: x=8, y=14
.
Done.
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