SOLUTION: the sum of a 2-digit number and the 2-digit number when the digits are reversed are 77 and the difference is 45. what are the 2 two digit numbers

Question 603822: the sum of a 2-digit number and the 2-digit number when the digits are reversed are 77 and the difference is 45. what are the 2 two digit numbers
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
the sum of a 2-digit number and the 2-digit number when the digits are reversed are 77 and the difference is 45.
what are the 2 two digit numbers
:
a = original 10's digit
b = units
:
(10a+b) + (10b+a) = 77
11a + 11b = 77
simplify, divide by 11
a + b = 7
:
"the difference is 45."
(10a+b) - (10b+a) = 45
10a - a - 10b + b = 45
9a - 9b = 45
Simplify, divide by 9
a - b = 5
:
Use elimination here
a + b = 7
a - b = 5
-----------adding eliminates b, find a
2a = 12
a = 6
then
6 + b = 7
b = 7 - 6
b = 1
:
61 is the number
:
:
Check 61 + 16 = 77
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