SOLUTION: How do I solve by using two equations and two variables? The sum of the digits of a two-digit number is 12. If 15 is added to the number, the result is 6 times the units digit.

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: How do I solve by using two equations and two variables? The sum of the digits of a two-digit number is 12. If 15 is added to the number, the result is 6 times the units digit.      Log On


   

Question 141370This question is from textbook Prentice hall algebra 1
: How do I solve by using two equations and two variables?
The sum of the digits of a two-digit number is 12. If 15 is added to the number, the result is 6 times the units digit. Find the number. This question is from textbook Prentice hall algebra 1

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = 10's digit
Let y = units digit
;
The two digit number: 10x + y
:
Write and equation for each statement:
:
"The sum of the digits of a two-digit number is 12."
x + y = 12
or
y = (12 - x) use for substitution
:
"If 15 is added to the number, the result is 6 times the units digit."
10x + y + 15 = 6y
:
10x + 15 = 6y - y
10x + 15 = 5y
:
Find the number.
Substitute (12-x) for y in the above equation
10x + 15 = 5(12 - x)
10x + 15 = 60 - 5y
10x + 5y - 60 - 15
15x = 45
x = 45%2F15
x = 3 is the 10's digit
then
12 - 3 = 9 is the units digit
:
Our number: 39
;
:
Check the solutions in the statement:
"If 15 is added to the number, the result is 6 times the units digit."
15 + 39 = 6(9)
54 = 54