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Question 910189: Five times the sum of the digits of a two-digit number is 13 less than the original number. If you reverse the digits in the two-digit number, four times the sum of its two digits is 21 less than the reversed two-digit number.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Five times the sum of the digits of a two-digit number is 13 less than the original number. If you reverse the digits in the two-digit number, four times the sum of its two digits is 21 less than the reversed two-digit number.
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Number:: 10t + u
Reverse: 10u + t
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Equations:
5(t+u) = 10t+u-13
4(t+u) = (10u+t)-21
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Rearrange:
-5t + 4u = -13
3t - 6u = -21
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Modify for elimination::
-15t + 12u = -39
-15t + 30u = 105
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18u = 144
u = 8
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Solve for "t":
-15t + 96 = -39
-15t = -135
t = 9
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Ans:: Number = 10t+u = 98
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Cheers,
Stan H.
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