Question

1. 1 / 1 points a gas - station sells three types of gas: regular for $2.80 a gallon, performance plus for $3.00 a gallon, and premium for $3.20 a gallon. on a particular day 5,900 gallons of gas were sold for a total of $17,140. three times as many gallons of regular as premium gas were sold. how many gallons of each type of gas were sold that day? regular 4200 gallons performance plus 300 gallons premium 1400 gallons 10. 1 / 1 points

Explanation:

Step1: Set up equations

Let $x$ be the number of gallons of Premium gas, $y$ be the number of gallons of Performance Plus gas, and $z$ be the number of gallons of Regular gas. We know that $z = 3x$. Also, $x + y+z=5900$ and $3.2x + 3y+2.8z=17140$. Substitute $z = 3x$ into the first - equation: $x + y+3x=5900$, which simplifies to $4x + y=5900$, so $y = 5900 - 4x$.

Step2: Substitute into the cost - equation

Substitute $z = 3x$ and $y = 5900 - 4x$ into the cost - equation $3.2x + 3y+2.8z=17140$. We get $3.2x+3(5900 - 4x)+2.8(3x)=17140$. Expand the equation: $3.2x + 17700-12x + 8.4x=17140$.

Step3: Combine like terms

Combine the $x$ terms: $(3.2x-12x + 8.4x)+17700=17140$. $(-8.8x + 8.4x)+17700=17140$. $-0.4x=17140 - 17700$. $-0.4x=-560$.

Step4: Solve for $x$

Divide both sides of the equation $-0.4x=-560$ by $-0.4$: $x=\frac{-560}{-0.4}=1400$.

Step5: Solve for $y$

Since $y = 5900 - 4x$, substitute $x = 1400$ into this equation: $y = 5900-4\times1400=5900 - 5600 = 300$.

Step6: Solve for $z$

Since $z = 3x$, substitute $x = 1400$ into this equation: $z = 3\times1400 = 4200$.

Answer:

Premium gas: 1400 gallons, Performance Plus gas: 300 gallons, Regular gas: 4200 gallons