You need to put oil into the gearbox of a rebuilt machine tool. The gearbox holds 16.3 liters of oil but the only oil you have is in 1-quart containers. How many of the 1-quart containers of oil will you need to fill the gearbox with 16.3 liters of oil?
A. 1
B. 5
C. 17
D. 18
E. 62
The correct answer and explanation is :
To solve this problem, we need to convert the volume of oil from liters to quarts and then determine how many 1-quart containers are needed.
Step 1: Convert Liters to Quarts
First, we need to know the conversion factor between liters and quarts. The standard conversion is:
1 liter = 1.057 quarts
The gearbox holds 16.3 liters of oil. To convert this to quarts, multiply the number of liters by the conversion factor:
$$
16.3 \, \text{liters} \times 1.057 \, \text{quarts/liter} = 17.23 \, \text{quarts}
$$
Step 2: Round Up to the Nearest Whole Number
Since we are using 1-quart containers and you can’t purchase a fraction of a container, we round 17.23 quarts up to the next whole number. This means you will need 18 quarts to fill the gearbox.
Step 3: Determine the Number of Containers
Since each container holds 1 quart, the number of containers you need is the same as the number of quarts required, which is 18.
Final Answer:
Therefore, the correct answer is D. 18.
Explanation:
- A quart is a unit of volume commonly used in liquid measurements, primarily in the United States.
- The liters-to-quarts conversion factor is critical here because the volume is initially given in liters, and the available oil comes in quarts.
- The problem is essentially asking how many quarts of oil are needed to fill a container that holds 16.3 liters, which we calculated by multiplying the volume in liters by the conversion factor to get the volume in quarts.
- Rounding up to the nearest whole number is necessary because you can’t purchase a fraction of a container, ensuring that you have enough oil to fully fill the gearbox.
Thus, 18 quarts of oil are needed, corresponding to 18 containers of oil.