SOLUTION: a number lies between 10 & 100. the number is 8 times the sum of its digits & when 45 is subtracted from the number the digits are reversed. what is the number?

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Question 887657: a number lies between 10 & 100. the number is 8 times the sum of its digits & when 45 is subtracted from the number the digits are reversed. what is the number?
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
U and T, the digits for UNITS and TENS.
The number is some variable 10%2AT%2BU. I am only guessing that the number is not 100.

Eight times the sum of its digits:
8%28U%2BT%29=U%2B10T

when 45 is subtracted from the number the digits are reversed:
U%2B10T-45=10U%2BT, think about this one carefully.

Simplify each equation.
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8U%2B8T=U%2B10T
7U=2T, not seem right.
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U-10U%2B10T-45=T
-9U%2B10T-T=45
-9U%2B9T=45
-U%2BT=5
T=U%2B5
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Try substituting for T in the first simplified equation.
7U=2T
7U=2%28U%2B5%29
7U=2U%2B10
5U=10
highlight%28U=2%29
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Again using 7U=2T, what is T?
7%2A2=2T
14=2T
highlight%28T=7%29
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The number is highlight%28highlight%2872%29%29.