Ez stop fast gas sold 10957 worth of gasoline yesterday. Redular grade sold for 2.30 a gallon and premium grade sold for 2.55 a gallon. If the station sold 420 more regular than premium, how many gallons of regular were sold
Represent the unknown with variables:
Let x = amount of premium grade gasoline sold in gallons
Let x+420 = amount of regular grade gasoline sold in gallons (according to the third statement)
Then we set up the equation. We know that the total worth of gasoline sold is 10,957. Therefore, we multiply the costs per each gallon of regular & premium grade by their respective amounts and get the total:
2.55x + (2.30)(x+420) = 10957
Solving for x,
2.55 + 2.3x + 966 = 10957
4.85x = 10957 - 966
4.85x = 9991
x = 2060 gallons of premium grade, and
x+420 = 2480 gallons of regular grade
Hope this helps~ :)
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Equations
To determine the number of gallons of regular gasoline sold, we need to use the information given in the question. Let's break down the information step by step:
1. The total value of gasoline sold yesterday was $10,957.
2. The regular grade was sold for $2.30 per gallon, and the premium grade was sold for $2.55 per gallon.
3. The station sold 420 more gallons of regular gasoline than premium gasoline.
Now, let's use this information to find the number of gallons of regular gasoline sold:
Step 1: Calculate the price difference per gallon between regular and premium gasoline:
$2.55 - $2.30 = $0.25
This means that for every gallon of premium gasoline, the regular gasoline is $0.25 cheaper.
Step 2: Calculate the total value of the premium gasoline sold at $2.55 per gallon:
Let's assume x represents the number of gallons of premium gasoline sold.
Value of premium gasoline = $2.55 * x
Step 3: Calculate the total value of the regular gasoline sold at $2.30 per gallon:
Value of regular gasoline = $2.30 * (x + 420)
Since the station sold $10,957 worth of gasoline, we can create the following equation:
$2.55 * x + $2.30 * (x + 420) = $10,957
Simplifying the equation:
2.55x + 2.30x + 966 = 10,957
4.85x = 9,991
x = 9,991 / 4.85
x ≈ 2,056.70
Since we cannot have a fraction of a gallon, the number of gallons of premium gasoline sold is approximately 2,056.
Step 4: Calculate the number of gallons of regular gasoline sold:
Number of gallons of regular gasoline = Number of gallons of premium gasoline + 420
Number of gallons of regular gasoline = 2,056 + 420 = 2,476
Therefore, approximately 2,476 gallons of regular gasoline were sold.