# Ratio Word Problem - Algebra

by Fatmir
(Mount Vernon, NY )

Two numbers are in the ratio 2 5. If 6 is subtracted from their sum, the result is 50. What is the larger number?

### Comments for Ratio Word Problem - Algebra

 Apr 22, 2012 Ratio Word Problem by: Staff Question: by Fatmir (Mount Vernon, NY) Two numbers are in the ratio 2 5. If 6 is subtracted from their sum, the result is 50. What is the larger number? Answer: x = smaller number y = larger number Two numbers are in the ratio 2 5 x:y = 2:5 Therefore, x/y = 2/5 If 6 is subtracted from their sum, the result is 50 x + y - 6 = 50 You now have two equations with two unknowns: 1st equation: x/y = 2/5 2nd equation: x + y - 6 = 50 Solve for x in the first equation x/y = 2/5 (x/y)*y = (2/5)*y x*(y/y) = (2/5)*y x*(1) = (2/5)*y x = (2/5)*y Substitute (2/5)*y for x in the 2nd equation x + y - 6 = 50 (2/5)*y + y - 6 = 50 Solve for y (2/5)*y + y - 6 + 6 = 50 + 6 (2/5)*y + y + 0 = 50 + 6 (2/5)*y + y = 50 + 6 (1 + 2/5)*y = 50 + 6 (7/5)*y = 50 + 6 (7/5)*y = 56 (5/7)*(7/5)*y = (5/7)*(56) (7/7)*(5/5)*y = (5/7)*(56) (1)*(1)*y = (5/7)*(56) y = (5/7)*(56) y = (5)*(56/7) y = (5)*(8) y = 40 Solve for x Substitute 40 for y in the 1st equation x/y = 2/5 x = (2/5)*40 x = 80/5 x = 16 >>> the final answer is: (the smaller number) x = 16 (the larger number) y = 40 Thanks for writing. Staff www.solving-math-problems.com

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