A gas station sells regular gas for $2.20 per gallon and premium gas for $2.70 a gallon. At the end of a business day 220 gallons of gas were sold and receipts totaled $519. How many gallons of each type of gas were sold?
I know its a linear equation. just cant find out how to put it in equation form..
Let x=number of gallons of regular sold
then 220-x=number of gallons of premium sold
Total receipt:
2.20x+2.70(220-x)=519
Solve for x.
Let's represent the number of gallons of regular gas sold as "x" and the number of gallons of premium gas sold as "y".
The total number of gallons sold is 220, so we have the equation:
x + y = 220 (Equation 1)
The total receipts from selling regular gas can be calculated by multiplying the price per gallon ($2.20) by the number of gallons sold (x). Similarly, the total receipts from selling premium gas can be calculated by multiplying the price per gallon ($2.70) by the number of gallons sold (y).
The total receipts for both types of gas combined is $519, so we have the equation:
2.20x + 2.70y = 519 (Equation 2)
Now, we have a system of equations with Equation 1 and Equation 2. To solve it, we can use substitution or elimination method. Let's use the elimination method:
Multiply Equation 1 by 2.20 to match the coefficient of x with that in Equation 2:
2.20(x + y) = 2.20(220)
2.20x + 2.20y = 484 (Equation 3)
Now, subtract Equation 3 from Equation 2 to eliminate x:
(2.20x + 2.70y) - (2.20x + 2.20y) = 519 - 484
0.50y = 35
y = 35 / 0.50
y = 70
Now that we know the value of y, we can substitute it back into Equation 1 to solve for x:
x + 70 = 220
x = 220 - 70
x = 150
Therefore, 150 gallons of regular gas and 70 gallons of premium gas were sold.
To solve this problem, you can set up a system of linear equations using the given information. Let's assume that x represents the number of gallons of regular gas sold, and y represents the number of gallons of premium gas sold.
From the given information, we know the following equations:
1) The total number of gallons sold: x + y = 220 (equation 1)
2) The total revenue from the gas sales: 2.20x + 2.70y = 519 (equation 2)
Equation 1 represents the fact that the total number of gallons sold (x + y) is equal to 220. Equation 2 represents the fact that the total revenue from the gas sales ($2.20 per gallon for regular gas and $2.70 per gallon for premium gas) is equal to $519.
Now, you have a system of two linear equations. To solve it, you can use different methods such as substitution or elimination.
Let's solve it using the substitution method:
1) Solve equation 1 for x: x = 220 - y.
2) Substitute the value of x in equation 2: 2.20(220 - y) + 2.70y = 519.
Simplify: 484 - 2.20y + 2.70y = 519.
Combine like terms: 0.50y = 35.
3) Solve for y: y = 35 / 0.50 = 70.
Now, we know that y = 70. Substitute this value back into equation 1 to find x:
x + 70 = 220,
x = 220 - 70 = 150.
Therefore, 150 gallons of regular gas and 70 gallons of premium gas were sold at the gas station.