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The sum of the two numbers is 54. If the larger is divided by the smaller, the quotient is 2 and the remainder is 3. find the numbers.

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Seikina25viz
The sum of the two numbers is 54. The larger number is 37 and the smaller number is 17. Now, if we divide the two, the answer is 2 with the remainder of 3. Is my answer correct?
let x=smaller number
54-x=larger number
..
(54-x)/x=2+3/x
LCD:x
54-x=2x+3
3x=51
x=17
54-x=37
smaller number=17
larger number=37