Question 551146
The value of a certain two digit number is 4 more than six times the sum of it's digits. If the digits are reversed, the resulting number is 18 less than the original number. What is the original number?
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let t=ten's digit
let u=unit's digit
original 2-digit number=10t+u
10t+u=6(t+u)+4 (two digit number is 4 more than six times the sum of it's digits)
10t+u=6t+6u+4
10t+u=10u+t+18 (digits are reversed, the resulting number is 18 less than the original number)
..
4t-5u=4
9t-9u=18
..
36t-45u=36
36t-36u=72
-9u=-36
u=4
4t-5u=4
4t=24
t=6
original number=64