If you take a particular two-digit number, reverse its digits to make a second two-digit number, and add these two numbers together, the sum will be 121. What i

Question

I do not understand this problem. It is not making sense to me.

Answer 1

This one can be slightly tricky.  The secret is to treat each digit of the number as its own variable, which can be anything from 1 to 9.

 

If x is the first digit and y the second, then the first number can be represented as

 

10x + y.

 

(For example, if our two-digit number were 93, x would be 9 and y would be 3.  93 is 90 + 3, or 10*9 + 1*3.)

 

The second number, reversing the digits, would be

 

10y + x.

 

The sum of the two numbers is then 10x + y + 10y + x, or 11x + 11y.

So, 11x + 11y = 121

x + y = 11.

 

This means that there's actually 8 possibilities for the original two-digit number.  (The equation itself gives a potentially infinite number of possibilities, but it's constrained by our desire that x and y only be integers between 1 and 9.)

The possibilities would be

29  (29 + 92 = 121)

38  (38 + 83 = 121)

47  (47 + 74 = 121)

And so forth.