SOLUTION: In a number of two digits, the sum of the digits is 14. If the digits are interchanged, the resulting number is 18 less than the original number. Find the number.

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Question 1054978: In a number of two digits, the sum of the digits is 14. If the digits are interchanged, the resulting number is 18 less than the original number. Find the number.
Answer by Theo(13342) (Show Source):
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let x equal the first digit of the original number.
let y equal the second digit of the original number.

the original number is equal to 10x + y.

if you reverse the digits, then the number with the digits reversed is equal to 10y + x.

x + y = 14

10x + y = 10y + x - 18

simplify the second equation to get:

9x - 9y = -18

solve for x in the first equation to get x = 14 - y

replace x with 14 - y in the second equation to get:

9 * (14 - y) - 9y = -18

simplify to get 126 - 9y - 9y = -18

combine like terms to get 126 - 18y = -18

add 18 to both sides of the equation and add 18y to both sides of the equation to get:

126 + 18 = 18y

combine like terms to get 144 = 18y

divide both sides of the equation by 18 to get 144/18 = y

simplify to get 8 = y

since x + y = 14, then x must be equal to 6.

x + y = 14 becomes 14 = 14 which is true.

10x + y = 10y + x - 18 becomes 60 + 8 = 80 + 6 - 18 which becomes 68 = 86 - 18 which becomes 68 = 68 which is true.

the original number is 10x + y which is equal to 68.

the number with the digits reversed is equal to 10y + x which is equal to 86.