SOLUTION: The sum of the digits of a two digit number is 9. The number is twice the product of its digits. Find the number.

Question 933311: The sum of the digits of a two digit number is 9. The number is twice the product of its digits. Find the number.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The sum of the digits of a two digit number is 9. The number is twice the product of its digits. Find the number.
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Let the number be 10t+u
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Equations:
t + u = 9
10t+u = 2tu
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Substitute for "t" and solve for "u":
10(9-u) + u = 2(9-u)u
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90 - 9u = 18u - 2u^2
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2u^2 - 27u + 90 = 0
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(2u-15)(u-6) = 0
u = 7.5 (extraneous because the answeer must be a whole number)
u = 6
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Solve for "t":
t + u = 9
t + 6 = 9
t = 3
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Ans: 10t+u = 36
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Cheers,
Stan H.
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