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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

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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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