SOLUTION: When the digits of a two-digit number are reversed, the new number is 9 more than the original number, and the sum of the digits of the original number is 11. What is the original
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Question 140535: When the digits of a two-digit number are reversed, the new number is 9 more than the original number, and the sum of the digits of the original number is 11. What is the original number? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! When the digits of a two-digit number are reversed, the new number is 9 more than the original number, and the sum of the digits of the original number is 11. What is the original number?
:
Let x = the 10's digit
Let y = the units digit (original number)
:
write an equation for the statement:
"When the digits of a two-digit number are reversed, the new number is 9 more than the original number,"
:
10y + x = (10x + y) + 9
10y - y = 10x - x + 9
9y = 9x + 9
simplify, divide equation by 9
y = x + 1
:
"the sum of the digits of the original number is 11."
x + y = 11
Substitute (x+1) for y
x + (x+1) = 11
2x = 11 - 1
x =
x = 5, then y = 6
:
What is the original number?
56
:
:
Check:
65 = 56 + 9
