Question 1040425
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!!!!!!
<pre>Let amount of regular, performance plus, and premium sold, be R, Q, and P, respectively
Then equation for amount sold = R + Q + P = 4,000 ----- eq (i)
Equation for sales: 2.85R + 3.1Q + 3.35P = 12,125 ------ eq (ii)
Also, R = 2P ------ eq (iii)
2P + Q + P = 4,000 ------ Substituting 2P for R in eq (i)
3P + Q = 4,000______Q = 4,000 - 3P ------- eq (iv)
2.85(2P) + 3.1Q + 3.35P = 12,125 ------ Substituting 2P for R in eq (ii)
5.7P + 3.1Q + 3.35P = 12,125
9.05P + 3.1Q = 12,125 ------- eq (v)
9.05P + 3.1(4,000 - 3P) = 12,125 ----- Substituting 4,000 - 3P for Q in eq (v)
9.05P + 12,400 - 9.3P = 12,125
9.05P - 9.3P = 12,125 - 12,400
- .25P = - 275
P, or amount of premium gas sold = {{{(- 275)/(- .25)}}}, or {{{highlight_green(matrix(1,2, "1,100", gallons))}}}

R = 2(1,100) ------- Substituting 1,100 for P in eq (iii)
R, or amount of regular gas sold = {{{highlight_green(matrix(1,2, "2,200", gallons))}}} 
 
Q = 4,000 - 3(1,100) ------- Substituting 1,100 for P in eq (iv)
Q = 4,000 - 3,300
Q, or amount of performance plus gas sold = {{{highlight_green(matrix(1,2, 700, gallons))}}}