SOLUTION: The sum of a two digit number is 15 . If the digits are reversed , the number formed is 27 less than the original number . Find the original number

Question 764518: The sum of a two digit number is 15 . If the digits are reversed , the number formed 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 a two digit number is 15.
If the digits are reversed, the number formed is 27 less than
the original number.
Find the original number
:
Let the two digits be a & b
then
10a+b = the original number
:
Write an equation for each statement
:
"The sum of a two digit number is 15"
a + b = 15
:
"If the digits are reversed, the number formed is 27 less than the original number"
10b + a = 10a + b - 27
Combine like terms on the right
0 = 10a - a - 10b + b - 27
9a - 9b = 27
simplify, divide by 9
a - b = 3
:
Use elimination with these two equations
a + b = 15
a - b = 3
-----------addition eliminates b, find a
2a = 18
a = 9
:
I'll let you find b, check your solutions in both statements

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