Question

The digits of a two-digit number sum to 8. When the digits are reversed, the resulting number is 18 less than the original

number. What is the original number?
35
OOOO
53

Answer 1

Explanation:

x + y = 8

10x + y is the original number

so 10y + x + 18 = 10x + y Subtract 10y and x from both sides

18 = 10x - x + y - 10y Combine the right

18 = 9x - 9y Divide by 9

2 = x - y

x - y = 2

x + y= 8 Add to find x

2x = 10 Divide by 2

x = 5

x + y = 8

5 + y = 8

y = 3

The original number is 53