Question

The sum of the two digits of a number is 16. The number formed by reversing the digits is 18 more than the original number. Determine the original number.

Let t = the tens digit, u = the units digit, and u + t = 16. Which of the following equations would complete the system?

9t - 9u = 18
9u - 9t = 18
tu = ut + 18

Answer 1

@sourwing?

Answer 2

10t + u = original number

when reversed:
10u + t = new number


new number = 18 + oringal number, so
10u + t = 18 + 10t + u

Answer 3

that's is for the first part. You try the second part

Answer 4

how did you get 10?

Answer 5

say you have 98. wouldn't 98 = 10(9) + 8? because the 9 is the tens digit

Answer 6

oh wait i get lol sorry

Answer 7

so isnt it the middle one

Answer 8

@mathmale will you help

Answer 9

I'll try! But it'll be a minute or two before I can get back to you.

Answer 10

ok thanks!

Answer 11

I haven't read all of the discussion you've had just recently. Would you mind telling me as accurately as you can what you need to know to solve this problem, and how I may be able to help with this?

Answer 12

If t=10's digit and u=1's digit, then tu represents the original number. It just so happens that t+u=16. Just supposing that t=7 and u=9, then t+u=16, right? tu would be 79 and ut would be 97. Give this some thought. Actually, I've just made educated guesses and believe that was enough to give me the answer: ut=the original number = 79.

Still, you must be able to write equations that lead you to the correct values of u and t.
I'm really sorry, but I need to get off my computer pronto. I hope these leads are sufficient to help you come up with proper equations for the identification of t and u.