Question 1015166
T=tens digit; U=units digit
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T*U=(1/3)(10T+U) .
Multiply each side by 3.
3TU=10T+U . Subtract 10T from each side.
3TU-10T=U
T(3U-10)=U . Divide each side by (3U-10).
T=U/(3U-10)
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T (tens digit) must an integer from 0 - 9 , so {{{U/(3U-10)}}}
must be an integer, and U must also be an integer from 0 - 9. 
The only values that satisfy both for U are 4 and 5
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For U=4:
T={{{U/(3U-10)=4/(3(4)-10)}}}={{{4/(12-10)=4/2}}}=2
ANSWER 1: One answer is 24.
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CHECK:
T*U=(1/3)(10T+U)
2*4=(1/3)(10(2)+4)
8=(1/3)(20+4)
8=(1/3)(24)
8=8
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For U=5:
T={{{U/(3U-10)=5/(3(5)-10)}}}={{{5/(15-10)=5/5}}}=1
ANSWER 2: Another answer is 15.
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CHECK:
T*U=(1/3)(10T+U)
1*5=(1/3)(10(1)+5)
5=(1/3)(10+5)
5=(1/3)(15)
5=5
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ANSWER: The number is 15 or 24