Verified Answer :

  • Convert 2 quarts to cups using the ratio 1 quart = 4 cups, resulting in \(2 \times 4 = 8\) cups.
  • Compare the values: 8 cups vs. 6 cups.
  • Since 8 cups > 6 cups, the larger volume is 2 quarts.
  • The final answer is \(\boxed{\text{a. } 2 \text{ quarts}}\).

Explanation

  1. Problem Analysis and Conversion Setup

We are tasked with comparing two quantities: \(2\) quarts and \(6\) cups. To make a valid comparison, both quantities must be expressed in the same unit. We know that in the US customary system, one quart is equivalent to \(4\) cups. Therefore, our objective is to convert \(2\) quarts into cups and compare it with \(6\) cups to determine which is greater.

  1. Calculating and Comparing the Volumes

Using the conversion factor where \(1 \text{ quart} = 4 \text{ cups}\), we calculate the volume of \(2\) quarts in terms of cups:
\[2 \text{ quarts} = 2 \times 4 \text{ cups} = 8 \text{ cups}\]
Now we have both quantities in cups: \(8\) cups and \(6\) cups. Since \(8 > 6\), it follows that \(2\) quarts is a greater volume than \(6\) cups.

  1. Conclusion

Since we have determined that \(8\) cups is more than \(6\) cups, it concludes that \(2\) quarts is the larger quantity. Thus, the correct option is a.
\(\boxed{\text{a. } 2 \text{ quarts}}\)

Examples

When you are cooking, you might encounter recipes that use different volume units like quarts and cups. Knowing the conversion factor—that 1 quart equals 4 cups—allows you to accurately adjust ingredients. For example, if a recipe calls for 2 quarts of water but you only have a measuring cup that marks volume in cups, you can easily calculate that you need 8 cups of water. This skill ensures your proportions are perfect every time you cook.

Related Questions