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# Advanced Math/Fractional Equation - Partial Solution / Explanation

Question
Two numbers, whose total is 73, is that the quotient obtained by dividing the larger by the smaller is 3 and the remaining is 13.

Let x = larger number

Let 73 - x = smaller number

x/73 - x = 3 + 13/73 - x

I don't understand the solution.  Thanks.

"Two numbers whose total is 73"
Let x and (73-x) represent the two numbers.

"dividing the larger number by the smaller gives a quotient of 3 and a remainder of 13"
Suppose x > 73-x, then x is the dividend and 73-x is the divisor.

dividend = (quotient·divisor)+remainder
x = 3·(73-x) + 13
x = 219-3x + 13
4x = 232
x = 58
73-x = 15

The numbers are 58 and 15.
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