Question 164608
The product of the two-digit number and its tens digit is 54. Find the number if the sum of the digits when added to the number gives a result of 36?
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Let the number be 10t+u where t is the tens digit and u is the ones digit.
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EQUATION:
t(10t+u) = 54
(t+u)+ 10t+u = 36
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Rearrange the equations:
10t^2 + tu = 54
11t + 2u = 36
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u = (36-11t)/2
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Substitute into the quadratic to get:
10t^2 + t[(36-11t)/2] = 54
20t^2 + 36t - 11t^2 = 108
9t^2 + 36t - 108 = 0
t^2 + 4t - 12 = 0
(t+6)(t-2) = 0
t = 2 (the tens digit is 2)
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u = (36-11*2)/2 = 7 (the units digit is 7)
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The number is 27
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Cheers,
Stan H.