Question

The difference between two natural numbers is 39. If the larger number is divided by the smaller one, then the quotient is 3 and the remainder is 11. The smaller number =

Answer 1

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Define x and y :
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Let one number be x and the other number will be x + 39

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Construct equation : 
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When the big number divided by the smaller number, the quotient is 3 with 11 remaining
⇒ $\dfrac{x + 39 - 11}{x} = 3$

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Solve x :
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$\dfrac{x + 39 - 11}{x} = 3$

$\dfrac{x + 28}{x} = 3$

$x + 28 = 3x$

$2x = 28$

$x = 14$

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Find the numbers:
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small number = x = 14

big number = x + 39 = 14 + 39 = 53

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Answer: The smaller number is 14.
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