Question

Find the two-digit number satisfying the following two conditions:

Answer 1

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Define x :
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Let the two digit number be 10x + y.

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Construct Equation :
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Four times the units digit is six less than twice the tens digit
⇒ 4y = 2x - 6
⇒2y = x - 3
⇒ x = 2y + 3

The number is nine less than three times the number obtained by reversing the digits.
⇒10x + y = 3(10y + x) - 9
⇒ 10x + y = 30y + 3x - 9
⇒ 7x = 29y - 9

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Solve for x and y :
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 x = 2y + 3 ----------------------- (1)
10x = 29y - 9  ------------------- (2)

Sub (1) into (2) :

7(2y + 3) = 29y - 9
14y + 21 = 29y - 9
15y = 30
y = 2 ------------------- Sub into (1)
x = 2(2) + 3
x = 7

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Find the number:
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Number = 10x + y = 10(2) + 7 = 27

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Answer: The 2-digit number is 27.
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