SOLUTION: The sum of two numbers is 69. If the larger is divided by the smaller, the quotient is 3 and the remainder is 9. Find the numbers. Here is what I have so far: Smaller =X lar

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Question 703594: The sum of two numbers is 69. If the larger is divided by the smaller, the quotient is 3 and the remainder is 9. Find the numbers.
Here is what I have so far:
Smaller =X
larger = 69-X
I know the answer is 54 and 15 because the homework is multiple choice but I do not know how to get there.
Thanks in advance.
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
Forget about the multiple choices given to you, and first analyze and solve.
Two numbers, x and y. Let x. First description gives x%2By=69.
Last description means, y%2Fx=3%2B9%2Fx -----was not appearing during editing so may look repeated-------

The rational equation, when multiply both sides by x, becomes y=3x+9.
A system of simple linear equations is now obtained:
3x-y=-9
x+y=69

ADDING second to first, yields 4x+0=60, giving us x=15. Then from x+y=69, we find y=54.