Question

The sum of the digits of a two-digit number is 11. When the digits are reversed, the new number is 27 more than the original number. Find the original number. Check your answer.

Answer 1

Answer: 47

Step-by-step explanation: To solve this problem, let's use t to represent our tens digit and u to represent our units digit so that the value of our number can be represented as 10t + u.

If we represent the value of our number as 10t + u, the value of the number with the digits reversed can be represented as 10u + t.

Since the first sentence states that the sum of the digits of a two-digit number is 11, that's t + u = 11.

Reading through our second sentence, when the digits are reversed, the new number is 27 more than the original number, that's 10u + t "is" which means equals 27 more than the original number that's 10t + u + 27.

So 10t + u = 10t + u + 27.

Before solving this system however, let's rearrange our second equation so that the t's and u's are on the same side by subtracting 10t and u from both sides to get 9u - 9t = 27 and when we rewrite our first equation above it, instead of writing it as t + u = 11, let's write it as t + u = 11 so that our u's and t's will match up in the system.

To solve this system, let's use addition so multiply the top equation by 9 to get 9u + 9t = 99 and 9u - 9t = 27 so that when we add the equations together the t's cancel and we get 18u = 126. Dividing both sided by 18, u = 7.

To find t, plug 7 back in for u in our first equation to get t + 7 = 11. Subtract 7 from both sides and t = 4.

Since our tens digit is 4 and our units is 7, our number must be 47.

I have also attached my work on a whiteboard.

Answer 2

11 = 9+2, 8+3, 7+4, 6+5 which make "two digit" numbers
that is 92, 29, 83, 38, 74, 47, 65, 56
Reversing digits is +27 more
the original number is 47,
47 + 27 = 47 + 10 + 10 + 7 = 67 + 8 = 77 - 2 = 74