SOLUTION: The sum of the digits of a certain 2-digit number is 13. When you reverse the number, the new number is 9 less than the original number. The difference between the 2 digits is 1. F

Question 271141: The sum of the digits of a certain 2-digit number is 13. When you reverse the number, the new number is 9 less than the original number. The difference between the 2 digits is 1. Find the original number.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The two digit number: 10x + y
:
The sum of the digits of a certain 2-digit number is 13.
x + y = 13
:
When you reverse the number, the new number is 9 less than the original number.
10y + x = 10x + y - 9
10y - y = 10x - x - 9
9y = 9x - 9
simplify, divide by 9
y = x - 1
Find the original number.
:
replace y in the 1st equation with (x-1)
x + (x-1) = 13
2x = 13 + 1
2x = 14
x = 7
then
y = 6
:
76 is the number
:
:
Check solution in the statement:
"When you reverse the number, the new number is 9 less than the original"
67 = 76 - 9
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