SOLUTION: the sum of the digits of the two-digit number is 12. the number with the digits interchanged is 20 more than 8 times the unit digit of the original number. find the original number

Question 936188: the sum of the digits of the two-digit number is 12. the number with the digits interchanged is 20 more than 8 times the unit digit of the original number. find the original number and the number interchanged.
please show me the solution. thank you.

Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
Let t = tens digit
u = units digit
10t + u = value of the number
10u + t = value of the number with digits reversed
we have two equations
t + u = 12
10u + t = 8u + 20
t + 2u = 20
subtract first equation form second equation
u = 8
t = 4
original number is 48 and the number interchanged is 84
84 = 64 +20 = 84
our answer checks

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