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The value of a fraction is 2/5. If the numerator is decreased by 2 and the denominator increased by 1, the resulting fraction is equivalent to 1/4. Find the numerator of the original fraction.

Correct Answer: 6
x/y = 2/5  = > 5x = 2y  = > 5x - 2y = 0 If you make the changes you get: (x - 2)/(y + 1) = 1/4 = > 4x - 8 = y + 1 = > 4x - y = 9 So you have two equations and can solve for x and for y: y = (5/2)x Substitute that into the 2nd equation to solve for x: 4x - (5/2)x = 9 = > 1.5x = 9 ∴x = 6 Substitute to solve for y: y = (5/2)6 ∴y = 15 x = 6, y = 15 

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