SOLUTION: A two digit number is eight times the sum of the digits. The number formed by reversing the digits is 45 less than the original number. Find the number.

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Question 878528: A two digit number is eight times the sum of the digits. The number formed by reversing the digits is 45 less than the original number. Find the number.
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
A two digit number is eight times the sum of the digits. The number formed by reversing the digits is 45 less than the original number. Find the number.
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let u=units digit
let t=tens digit
..
10t+u=8(u+t)
10u+t-45=10t+u
..
10t+u=8u+8t
2t=7u
t=7u/2
..
10u+t=10t+u-45
sub 7u/2 for t
10u+7u/2=10(7u/2)+u-45
mult. by LCD=2
20u+7u=70u+2u-90
45u=90
u=2
t=7u/2=14/2=7
number: 10t+u=70+2=72