There are two 2digit numbers that satisfy the following conditions:

(1) each number has the same digits;

(2) the sum of the digits in each number is 10;

(3) the difference between the two numbers is 54.

What are the two numbers?

a. The numbers 58 and 85 are 2digit numbers that have the same digits, and the sum of the digits in each number is 13. Find two 2digit numbers such that the sum of the digits is 10 and both numbers have the same digits. 64 and(,,,,,,?)

b. Since there are only 9 two-digit numbers whose digits have a sum of 10, the problem can be easily solved by guessing. What is the difference of your two 2digit numbers from part a?

c. Continue to guess and check. Which pair of numbers has a difference of 54? (....?) and (,,,,.?)

d. This problem can be extended by changing the requirement that the sum of the two digits equals 10. Solve the problem for the case in which the digits have a sum of 12 and a difference of 54. (...?) and (,,,?)