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

Answer:

Step-by-step 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.