SOLUTION: I'm not sure if this is a mixture equation, but: The sum of the digits of a two digit number is 11. The number obtained by reversing the order of the digits is 27 less than the ori
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Question 127260: I'm not sure if this is a mixture equation, but: The sum of the digits of a two digit number is 11. The number obtained by reversing the order of the digits is 27 less than the original number. Find the original number.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The sum of the digits of a two digit number is 11. The number obtained by reversing the order of the digits is 27 less than the original number. Find the original number.
:
Let x = the original number 10's digit
Let y = the original number units digit
:
Write an equation for each statement:
:
"The sum of the digits of a two digit number is 11."
x + y = 11
or
y = (11 - x); will use this for substitution
:
"number obtained by reversing the order of the digits is 27 less than the original number."
10y + x = 10x + y - 27
:
10y - y = 10x - x - 27; some basic algebra operations
:
9y = 9x - 27
:
y = x - 3; simplified, divided equation by 9
:
Find the original number.
:
Substitute (11-x) for y in the above equation
11 - x = x - 3
:
11 + 3 = x + x
:
14 = 2x
:
x = 7 is the 10's digit
then
11 - 7 = 4 is the units digit
:
74 is the original number
:
Check solution using the statement:
"number obtained by reversing the order of the digits is 27 less than the original number."
47 = 74 - 27; confirms our solution
:
:
Could you follow what we did here? This is a good method to use on all these type of problems.
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