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2 years ago

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

1 answer:

lina2011 [118]2 years ago

4 0

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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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<span>Four times the units digit is six less than twice the tens digit
</span>⇒ 4y = 2x - 6
⇒2y = x - 3
⇒ x = 2y + 3

<span>The number is nine less than three times the number obtained by reversing the digits.
</span>⇒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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