Brent received two bills with his monthly gasoline statement. One bill for $92.30 showed he had bought 66L of gasoline and two liters of oil, while the other bill showed he had bought 75L of gasoline and one liter of oil for $100.75. If the price of gasoline and oil remained the same for both purchases, what was the cost per liter of gasoline and per liter of oil?

Use similar process to previous post.

Brent received two bills with his monthly gasoline statement. One bill for $92.30 showed he had bought 66L of gasoline and two liters of oil, while the other bill showed he had bought 75L of gasoline and one liter of oil for $100.75. If the price of gasoline and oil remained the same for both purchases, what was the cost per liter of gasoline and per liter of oil?

To find the cost per liter of gasoline and per liter of oil, we need to divide the total cost of each purchase by the total liters bought in each purchase.

Let's calculate the cost per liter of gasoline for both purchases:

For the first purchase:
Total cost = $92.30
Gasoline bought = 66L
Oil bought = 2L

To find the cost per liter of gasoline, we will subtract the cost of the oil from the total cost and then divide it by the liters of gasoline bought.
Gasoline cost = (Total cost - Cost of oil) / Gasoline bought
Gasoline cost = ($92.30 - $X) / 66L, where $X is the cost of oil.

For the second purchase:
Total cost = $100.75
Gasoline bought = 75L
Oil bought = 1L

Similarly, we will use the formula to find the cost per liter of gasoline for the second purchase.
Gasoline cost = (Total cost - Cost of oil) / Gasoline bought
Gasoline cost = ($100.75 - $X) / 75L, where $X is the cost of oil.

Since the price of gasoline and oil remained the same for both purchases, the cost per liter of gasoline in both purchases should be the same. Therefore, we can set the two equations equal to each other:

($92.30 - $X) / 66L = ($100.75 - $X) / 75L

Now, let's solve this equation to find the value of $X, which represents the cost of oil.

First, cross-multiply to eliminate the denominators:
75L * ($92.30 - $X) = 66L * ($100.75 - $X)

Expanding the equation:
75L * $92.30 - 75L * $X = 66L * $100.75 - 66L * $X

Rearranging the equation:
75L * $X - 66L * $X = 66L * $100.75 - 75L * $92.30

Combining like terms:
9L * $X = 66L * $100.75 - 75L * $92.30

Now, divide by 9L to isolate $X:
$X = (66L * $100.75 - 75L * $92.30) / 9L

Now, calculate the value of $X using the given numbers:
$X = (66L * $100.75 - 75L * $92.30) / 9L

After evaluating this expression, you will find the cost of oil, $X.

Finally, we can find the cost per liter of gasoline by substituting the value of $X into the equation for either purchase:

Gasoline cost = (Total cost - Cost of oil) / Gasoline bought

Similarly, to find the cost per liter of oil, divide the cost of oil by the liters bought.

By following these steps and performing the necessary calculations, we can determine the cost per liter of gasoline and per liter of oil.