The sum of a 2-digit number and the 2-digit number when the digits are reversed is 77. If the difference of the same two numbers is 45, what are the two 2-digit numbers?
Let t be the ten's digit of the original number and u be the unit's digit of the original number.
This means that the original number is 10·t + u.
Reversing the digits, the new number is 10·u + t
Adding these numbers together, we get a sum of 77: (10t + u) + (10u + t) = 77
Simplifying: 11t + 11u = 77
Dividiing each term by 11: t + u = 7
Subtracting these numbers, we get a difference of 45: (10t + u) - (10u + t) = 45
Simplifying: 9t - 9u = 45
Dividing each term by 9: t - u = 5
Combining these two equations: t + u = 7
t - u = 5
Adding down the columns: 2t = 12
Divide by 2: t = 6
Substituting back into the equation t + u = 7 ---> 6 + u = 7 ---> u = 1
You'll need to write the two numbers ...