Gas Station A gas station sells three types of gas: Regular for $3.00 a gallon, Performance Plus for $3.20 a gallon, and Premium for $3.30 a gallon. On a particular day 6500 gallons of gas were sold for a total of $20,050. Three times as many gallons of Regular as Premium gas were sold. How many gallons of each type of gas were sold that day?
The number of gallons of each type of gas sold.
Answer to Problem 40E
The number of gallons sold of regular type is 4500, performance type is 500 and premium type is 1500.
Explanation of Solution
Given:
Total number of gallons sold on a particular day are 6500 and total selling amount is
The selling cost of regular type is
The selling cost of performance plus type is
The selling cost of premium type is
Calculation:
Let the number of gallons of regular type gas sold is x,
The number of gallons of performance plus gas sold is y and,
The number of gallons of premium type sold is z.
To get the number of gallons were sold on a particular day, convert all facts into equations.
As, the total number of gallons sold on a particular day is 6500,
The equation is,
The selling cost of regular, performance plus and premium per gallon is
The equation here is,
Gas station sold three times as many gallons of regular as premium,
The equation is,
Thus, the system of equation is,
Substitute 3z for x into equation (1) to get the solution of system of equations,
Substitute 3z for x into equation (2) to get the solution of system of equations,
Now, from the equation (4) calculate the value of y in terms of z,
Substitute
Substitute 1500 for z into equation (6) to get the value of y,
Substitute 1500 for z into equation (3),
The value of x is 4500, y is 500 and z is 1500.
Therefore, the number of gallons sold of regular type is 4500, performance type is 500 and premium type is 1500.
Chapter 10 Solutions
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