SOLUTION: Company A Spent a total of $11 million on advertising in fiscal year 2010, 2011, and 2012. The amount spent in 2012 was three times the amount spent in 2010. The amount spent in 2

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons  -> Linear Equations Lesson -> SOLUTION: Company A Spent a total of $11 million on advertising in fiscal year 2010, 2011, and 2012. The amount spent in 2012 was three times the amount spent in 2010. The amount spent in 2      Log On


   



Question 948381: Company A Spent a total of $11 million on advertising in fiscal year 2010, 2011, and 2012. The amount spent in 2012 was three times the amount spent in 2010. The amount spent in 2011 was $3 million less than the amount spent in 2012. How much was spent on advertising each year.
My attempt to set-up the system:
x + y + z = 11
y - z = 3
z = 3x

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Company A Spent a total of $11 million on advertising in fiscal year 2010,+2011, and 2012.
your attempt to set-up the system was perfect, system just need to be solved
so,
in year 2010 company spent x million,
in year 2011 company spent y million,
in year 2012 company spent z million,
total: x%2By%2Bz=11........eq.1
The amountz spent in 2012 was three times the amount x spent in 2010.
z=3x........eq.2
The amounty spent in 2011 was $3 million less than the amount z spent in 2012.
y=z-3 ........eq.3
solve the system:
x%2By%2Bz=11........eq.1
z=3x........eq.2
y=z-3 ........eq.3
-----------------------------------------
start with y=z-3 ........eq.3 substitute z%7D%7D+from+eq.2%0D%0A%7B%7B%7By=3x-3.......3a
go to
x%2By%2Bz=11........eq.1 substitute z%7D%7D+from+eq.2+and+%7B%7B%7By from eq.3a
x%2B3x-3%2B3x=11...... solve for x
7x=11%2B3
7x=14
x=14%2F7
highlight%28x=2%29
go to y=3x-3.......3a substitute 2%7D%7D+for++%7B%7B%7Bx%7D%7D%0D%0A%0D%0A%7B%7B%7By=3%2A2-3
y=6-3
highlight%28y=3%29
go to z=3x........eq.2 substitute 2%7D%7D+for++%7B%7B%7Bx%7D%7D%0D%0A%0D%0A%7B%7B%7Bz=3%2A2
highlight%28z=6%29
so, each year on advertising was spent:
in year 2010 company spent 2 million,
in year 2011 company spent 3 million,
in year 2012+company spent 6 million,