Question

If the numerator and denominator of a fraction are both increased by 5, the resulting fraction is equivalent to 2/3. However, if the numerator and denominator are both decreased by 5, the resulting fraction is equivalent to 3/7. What is the fraction?

Answer 1

(x+5)/(y+5) = 2/3

(x-5)/(y-5) = 3/7
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2 y + 10 = 3 x + 15
3 y - 15 = 7 x - 35
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3 x - 2 y = -5
7 x - 3 y = 20
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9 x - 6 y = -15
14 x -6 y = 40
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-5 x = -55
x = 11
then 33-2y = -5
2 y = 38
y = 19

11/19