Question

A car got 33 miles per gallon using gasoline that cost $2.95 per gallon. Approximately what was the cost, in dollars, of the gasoline used in driving the car 350 miles?

• A. $10
• B. $20
• C. $30
• D. $40
• E. $50

Hint:

When a question uses the word "approximately" and the answer choices are far apart, rounding the numbers in the problem to "compatible numbers" (numbers that are easy to compute with) is a very effective and time-saving strategy.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This is a multi-step problem that requires calculating the total amount of fuel consumed and then finding the total cost based on the price per unit of fuel. The word "approximately" indicates that we can use estimation to find the answer.
Step 2: Key Approach:
1. Calculate the total gallons of gasoline needed for the trip.
2. Calculate the total cost by multiplying the total gallons by the cost per gallon.
3. Use approximation to simplify the calculations.
Step 3: Detailed Explanation:
Part 1: Calculate Gallons Used
The car drives 350 miles and gets 33 miles per gallon.
\[ \text{Gallons Used} = \frac{\text{Total Miles}}{\text{Miles Per Gallon}} = \frac{350}{33} \] Part 2: Calculate Total Cost
The cost of gasoline is $2.95 per gallon.
\[ \text{Total Cost} = (\text{Gallons Used}) \times (\text{Cost Per Gallon}) = \left(\frac{350}{33}\right) \times 2.95 \] Part 3: Estimation
The answer choices are spread out, so estimation is a good strategy. Let's round the numbers to make the calculation easier.
- Round the fuel efficiency from 33 mpg to a number that divides 350 easily. 35 mpg is a close and convenient number, but let's stick with the PDF's approach.
- Round 33 mpg down to 30 or up to 35. Let's use the numbers given. 33 is close to 35. Or we can see that 350/33 is a bit more than 10 because 33 * 10 = 330.
- Round the cost from $2.95 per gallon up to $3.00 per gallon.
Now let's recalculate the approximate cost:
\[ \text{Approximate Gallons} \approx \frac{350}{33} \approx 10.6 \text{ gallons} \] \[ \text{Approximate Cost} \approx 10.6 \times $3 = $31.80 \] Alternatively, using the PDF's direct approximation:
\[ \text{Approximate Cost} \approx \left(\frac{350}{33}\right) \times 3 \approx (10) \times 3 = $30 \] This result, $31.80 or $30, is very close to $30.
Step 4: Final Answer:
The estimated cost is approximately $30. This matches option (C).