In a rational number, twice the numerator is 2 more than the denominator. If 3 is added to both the numerator and the denominator the new fraction is 2/3. Find the original fraction?
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A / B
2 A = B + 2 -- -eq 1
(A + 3 ) / ( B + 3) = 2 / 3
cross multiply to get 3A + 9 = 2 B + 6 => 3A = 2 B - 3 ---- eq 2
Multiply equation 1 by 2 and subtract eq 2
4 A - 3 A = 2B -2 B + 4 + 3 => A = 7
B = 12
2 A = B + 2 -- -eq 1
(A + 3 ) / ( B + 3) = 2 / 3
cross multiply to get 3A + 9 = 2 B + 6 => 3A = 2 B - 3 ---- eq 2
Multiply equation 1 by 2 and subtract eq 2
4 A - 3 A = 2B -2 B + 4 + 3 => A = 7
B = 12
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