# A fraction has a value 2/3. If 4 is added to the numerator and the denominator is decreased by 2, the resulting fractions have the value 6/7. What is the original fraction? (Let x be the numerator and y be the denominator)

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1. numerator --- x
denominator --- y

x/y = 2/3
2y = 3x
y = 3x/2

new fraction:
(x+4)/(y-2) = 6/7
6y - 12 = 7x + 28
6y = 7x + 40
3(2y) = 7x+40
3(3x) = 7x + 40
2x = 40
x = 20
y = 30

the non-reduced fraction was 20/30

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