SOLUTION: Two numbers are in the ratio of 5:8 their difference is 45. What is the smaller number?

Question 1105654: Two numbers are in the ratio of 5:8 their difference is 45. What is the smaller number?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
x is the first number.
y is the second number.

x/y = 5/8
x = 5/8 * y

y - x = 45 (because y is bigger than x, the difference will be positive).

since x = 5/8 * y , then y - x = 45 becomes y - 5/8 * y = 45 which becomes (8-5)/8 * y = 45 which becomes 3/8 * y = 45

multiply both sides of this equation by 8/3 to get y = 45 * 8/3 which results in y = 15 * 8 which results in y = 120.

when y = 120, x = 5/8 * y becomes x = 5/8 * 120 which becomes x = 5 * 15 which results in x = 75.

you have x = 75 and y = 120.

x/y = 75/120 which becomes x/y = 15/24 which becomes x/y = 5/8.

you get x/y = 5/8 which can be written as x:y = 5:8 which is what you were given to start with.

y - x = 120 - 75 = 45 which is also what you were given to start with.

the solution is confirmed to be good.

y is the biggest number.
x is the smallest number.

the solution is that the smallest number is 75.

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