Jan 20, 2018
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The sum of the digits of a two-digit number is 14. If the digits are reversed, the number is 18 less than the original number. Find the original number.
Let x = the 10's digit Let y = the units : 10x + y = the original two digit number : The sum of the digits of a two-digit number is 14. x + y = 14 : "If the digits are reversed, the number is 18 less than the original number." Rev no. = orig no. - 18 10y + x = 10x + y - 18 10y - y = 10x - x - 18 9y = 9x - 18 simplify, divide by 9 y = x - 2 : In the sum equation replace y with (x-2) x + (x-2) = 14 2x = 14 + 2 2x = 16 x = 8 obviously y = 6 : 86 is the original number : : Check solution in the statement: "If the digits are reversed, the number is 18 less than the original number." 68 = 86 - 18