SOLUTION: A two digit number is three less than seven times the sum of its digits. if the digits are reversed, the new number is 18 less than the original number. what is the original number

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Question 467186: A two digit number is three less than seven times the sum of its digits. if the digits are reversed, the new number is 18 less than the original number. what is the original number?
Answer by stanbon(75887) About Me  (Show Source):
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A two digit number is three less than seven times the sum of its digits. if the digits are reversed, the new number is 18 less than the original number. what is the original number?
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Let the number be 10t+u
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Equation:
10t+u = 7(t+u)-3
10u+t = 10t+u-18
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Rearrange:
3t -6u = -3
9u-9t = -18
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Modify:
t - 2u = -1
-t+ u = -2
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Add and solve for "u":
-u = -3
u = 3
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solve for "t":
t-2u = -1
t-6 = -1
t = 5
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Original Number: 10*5+3 = 53
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Cheers,
Stan H.