Sophie's favorite number is a two-digit number. If she reverses the digits, the result is 45 less than her favorite number. The sum of the digits in her favorite number is 11. What is Sophie's favorite number?

Creampuff Jun 27, 2020

#1**+1 **

10 x + y = 45 + 10y + x and x+y = 11 or y = 11-x sub this into the first equation

10x + 11-x = 45 + 10(11-x) + x and solve for 'x'

9x + 11 = 45 +110-9x

18x = 144

x = 8 then y = 3 favorite number is 83 reversed = 38 which is 45 less than 83

ElectricPavlov Jun 27, 2020