Question 201829This question is from textbook Algebra Structure and Method
: Solve usingthe 5 step method
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 orginal number is 11. What is the original number?
This question is from textbook Algebra Structure and Method
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?
:
Two digits:
x = the 10's digit
y = units digit
:
The original number; 10x + y
:
"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 by 9
y = x + 1
:
"the sum of the digits of the original number is 11."
x + y = 11
Replace y with (x+1)
x + x + 1 = 11
2x = 10
x = 5
then
y = 5 + 1
y = 6
:
56 = the original number
:
Check solution in the statement:
"when the digits of a two-digit number are reversed, the new number is
9 more than the original number,"
65 = 56 + 9
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