SOLUTION: a two-digit number is equal to 3 times the sum of its digits.if the number obtained by reversing the digits is divided by the original number, the quotient is 2 and the remainder i

Question 140778: a two-digit number is equal to 3 times the sum of its digits.if the number obtained by reversing the digits is divided by the original number, the quotient is 2 and the remainder is 1. Find the original number
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
a two-digit number is equal to 3 times the sum of its digits.
Eq.: 10t+u = 3(t+u)
Rearrange:
7t - 2u = 0
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if the number obtained by reversing the digits is divided by the original number, the quotient is 2 and the remainder is 1.
Eq.: (10u+t)/(10t+u) = 2 + 1/(10t+u)
Rearrange:
Multiply thru by 10t+u to get:
10u+t = 2(10t+u) + 1
10u+t = 20t+2u + 1
19t-8u=-1
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System:
7t-2u = 0
19t-8u= -1
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Using Matrix methods:
t =
u =
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I do not get whole number solutions for t and u.
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Cheers,
Stan H.

Find the original number.
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