SOLUTION: The sum of the digits of a two-digit number is 7. The original two-digit number is 3 less than 4 times the number with its digits reversed. Find the original two-digit number.

Question 148461: The sum of the digits of a two-digit number is 7. The original two-digit number is 3 less than 4 times the number with its digits reversed. Find the original two-digit 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 7.
The original two-digit number is 3 less than 4 times the number with its digits reversed.
Find the original two-digit number.
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Let the original number be 10t+u where t is the tens digit and u is the units digit.
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EQUATIONS:
t + u = 7
10t+u = 4(10u+t)-3
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Rearrange:
t + u = 7
6t -39u = -3
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Modify:
6t + 6u = 42
6t - 39u = -3
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Subtract to solve for "u":
45u = 45
u = 1
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Substitute into t+u = 7 to solve for "t":
t+1 = 7; t=6
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Original Number: 61
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Cheers,
Stan H.

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