SOLUTION: Two 2-digit numbers have the same digits. their sum is 77 and their difference is 27. what are the numbers?

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Question 341482: Two 2-digit numbers have the same digits. their sum is 77 and their difference is 27. what are the numbers?
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
Make the numbers xy and yx. Let the larger number be xy.
10x+y + 10y+x = 77
10x+y -(10y+x)= 27
10x+y -10y-x = 27
.
11x + 11y = 77
09x - 09y = 27
.
99x + 99y = 693
99x - 99y = 297
----------------add
198x=990
.
x=5
.
10x+y + 10y+x = 77
50+y + 10y+5 = 77
55+11y=77
11y=22
y=2
.
Ed