Question 1040425
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QUESTION 2:
A gas station sells three types of gas: Regular for $2.85 a gallon, Performance Plus for $3.10 a gallon, and Premium for $3.35 a gallon. 
On a particular day 4000 gallons of gas were sold for a total of $12,125. 
Two times as many gallons of Regular as Premium gas were sold. How many gallons of each type of gas were sold that day?
I came up with the following system:
x+y+z=4000
2.85x+3.10y+3.35z=12125
x=2x
I tried using matrices but the answers I get do not work when plugged back into the system. These problems confuse the heck out of me!


THANK YOU!!!!!!
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The equation x = 2x is incorrect. It should be x = 2z.

<pre> 
So your system is

    x +     y +     z =  4000,   (1)
2.85x + 3.10y + 3.35z = 12125,   (2)
x = 2z.                          (3)

or

    x +     y +   x/2      =  4000,   (1')
2.85x + 3.10y + 3.35*(x/2) = 12125    (2')

(no "z". "z" is just excluded).  Multiply (1') and (2') by 2 (both sides) and collect the like terms.

3x    + 2y    =  8000,       (3)
9.05x + 6.20y = 24250.       (4)

I just did enough for you :=).

Can you complete on your own from this point?

Apply the substitution method. Express x from (3) an then substitute into (4).   Good luck !

Let me know if you still have problems.
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