The sum of the digits of a certain two-digit number is 16. Reversing its digits increases the number

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The sum of the digits of a certain two-digit number is 16. Reversing its digits increases the number by 18. What is the number?


Let x and (16-x) represent the original ten and units digits respectively

Reversing its digits increases the number by 18

Set up the relational equation
[10x + (16-x)] + 18 = 10(16 - x) + x

Solving for x
9x + 34 = 160 - 9x

Combine like terms
18x = 126

Divide each side of the equation by 18
18x/18 = 126/18
x = 7

So 16 - x = 16 - 7 = 9
The first number is 79, the other number is 97. and 97 - 79 = 18 so we match up.
The number in our answer is 79