Question

The sum of the digits of a two-digit number is 11. When the digits are reversed, the new number is 45 more than the original number. Find the original number. Check your answer.

Answer 1

Explanation:

Let the 10s digit = x

Let the units digit = y

x +y = 11 Sum of the digits = 11

10x + y + 45 = 10y + x Reversed number is 45 more than original #

10x - x + y + 45 = 10y We subtracted x from both sides.

9x + y + 45 = 10y Subtract y from both sides.

9x + 45 = 10y - y Combine the right

9x + 45 = 9y

Put x + y = 11 into the equation just found.

9x + 45 = 9(11 - x) divide through by 9

x + 45/9 = 11 - x add x to both sides

2x + 5 = 11 Subtract 5 from both sides

2x = 11 - 5

2x = 6 Divide by 2

x = 6/2

x = 3

x + y = 11

3 + y = 11

y = 11 - 3

y = 8

Now check it out.

the original number is 38

the new number is 83 which the digits are reversed.

83 - 38 = 45 just as it should.