document.write( "Question 1040425: QUESTION 2:
\n" ); document.write( "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.
\n" ); document.write( "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?
\n" ); document.write( "I came up with the following system:
\n" ); document.write( "x+y+z=4000
\n" ); document.write( "2.85x+3.10y+3.35z=12125
\n" ); document.write( "x=2x
\n" ); document.write( "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!\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "THANK YOU!!!!!! \n" ); document.write( "

Algebra.Com's Answer #655276 by MathTherapy(10552) $\"\"$ $\"About$

You can put this solution on YOUR website!
QUESTION 2:
\n" ); document.write( "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.
\n" ); document.write( "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?
\n" ); document.write( "I came up with the following system:
\n" ); document.write( "x+y+z=4000
\n" ); document.write( "2.85x+3.10y+3.35z=12125
\n" ); document.write( "x=2x
\n" ); document.write( "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!\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "THANK YOU!!!!!!
\n" ); document.write( "

Let amount of regular, performance plus, and premium sold, be R, Q, and P, respectively
\n" );
document.write( "Then equation for amount sold = R + Q + P = 4,000 ----- eq (i)
\n" );
document.write( "Equation for sales: 2.85R + 3.1Q + 3.35P = 12,125 ------ eq (ii)
\n" );
document.write( "Also, R = 2P ------ eq (iii)
\n" );
document.write( "2P + Q + P = 4,000 ------ Substituting 2P for R in eq (i)
\n" );
document.write( "3P + Q = 4,000______Q = 4,000 - 3P ------- eq (iv)
\n" );
document.write( "2.85(2P) + 3.1Q + 3.35P = 12,125 ------ Substituting 2P for R in eq (ii)
\n" );
document.write( "5.7P + 3.1Q + 3.35P = 12,125
\n" );
document.write( "9.05P + 3.1Q = 12,125 ------- eq (v)
\n" );
document.write( "9.05P + 3.1(4,000 - 3P) = 12,125 ----- Substituting 4,000 - 3P for Q in eq (v)
\n" );
document.write( "9.05P + 12,400 - 9.3P = 12,125
\n" );
document.write( "9.05P - 9.3P = 12,125 - 12,400
\n" );
document.write( "- .25P = - 275
\n" );
document.write( "P, or amount of premium gas sold = , or \r
\n" );
document.write( "\n" );
document.write( "R = 2(1,100) ------- Substituting 1,100 for P in eq (iii)
\n" );
document.write( "R, or amount of regular gas sold =  
\n" );
document.write( " 
\n" );
document.write( "Q = 4,000 - 3(1,100) ------- Substituting 1,100 for P in eq (iv)
\n" );
document.write( "Q = 4,000 - 3,300
\n" );
document.write( "Q, or amount of performance plus gas sold =  \n" );
document.write( "

\n" );