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The sum of a two-digit number and the number formed by interchanging its digits is 110. If 10 is subtracted from the first number, the new number is 4 more

than 5 times the sum of the digits in the first number. Find the first number.


> 11x+11y=110
> x+y=10 ----------1
>5x-4y=14 --------2
(1) * 4
=4x+4y=40 --------1*
 therefore, x=6
substituting for x in 1
y=10-6 = 4
therefore: x=6 and y=4 so the first number is 64.
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