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Chapter 8: Problem 72

A recipe for punch calls for 6 c of apple juice. A bottle of juice has 2 qt. Is there enough juice in the bottle for the recipe?

Short Answer

Expert verified
Yes, there is enough juice.

Step by step solution

01

- Understand the Problem

Determine the amount of apple juice needed and the amount available in different units.
02

- Convert Quarts to Cups

Convert the volume of apple juice from quarts to cups. There are 4 cups in a quart.
03

- Perform the Calculation

Multiply the number of quarts by the number of cups per quart: 2 qt * 4 c/qt = 8 c
04

- Compare Amounts

Compare the converted amount of 8 cups to the required 6 cups for the recipe.
05

- Conclude

Determine if 8 cups is sufficient for the recipe which requires 6 cups.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

volume conversion
Volume conversion involves changing a quantity expressed in one unit of volume to an equivalent quantity in another unit. For instance, in the given problem, we need to convert the volume of apple juice from quarts to cups to ensure compatibility with the recipe's measurements. The conversion factor is essential here. Knowing that 1 quart (qt) equates to 4 cups (c) is crucial for correctly transforming the volume units.
measurement units
Measurement units are standardized quantities used to give accurate descriptions of other quantities. In the context of volume, units like quarts and cups are common in recipes. Understanding these units and the conversion factor, like how 1 quart (qt) is equal to 4 cups (c), allows for seamless transitions between different units of measurement. This understanding ensures portions and ratios are maintained accurately, which is vital in following recipes or any other practical application.
step-by-step solutions
Solving unit conversion problems systematically ensures clarity and accuracy. Let's break down the solution for our example:

  • First, understand that we need to determine if 2 quarts of apple juice is enough to meet the recipe's requirement of 6 cups.

  • Next, convert quarts to cups using the known conversion: 2 quarts * 4 cups/quart = 8 cups.

  • Then, compare the converted amount of 8 cups to the required 6 cups.

  • Finally, conclude that 8 cups are more than sufficient for the recipe that requires 6 cups of apple juice.
mathematical reasoning
Mathematical reasoning is the process of thinking logically to solve a problem. It involves understanding and employing the right mathematical concepts and processes. In our exercise, we use mathematical reasoning to convert and compare units. Here鈥檚 the approach:

  • Recognize that the units given (quarts) need to be converted into the units required by the recipe (cups).
  • Apply the conversion factor (1 quart = 4 cups).
  • Multiply the volume in quarts by the conversion factor to get the volume in cups.
  • Finally, compare the converted volume to the volume required and conclude whether it meets the requirement.
This logical, structured approach ensures accurate and valid results.

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Most popular questions from this chapter

A contractor plans to construct a cement patio for one of the houses that he is building. The patio will be a square, 25 ft by 25 ft. After the contractor builds the frame for the cement, he checks to make sure that it is square by measuring the diagonals. Use the Pythagorean theorem to determine what the length of the diagonals should be if the contractor has constructed the frame correctly. Round to the nearest hundredth of a foot.

The measure of an angle is given. Find the measure of the supplement. $$179^{\circ}$$

A tennis court is \(120 \mathrm{ft}\) long and \(60 \mathrm{ft}\) wide. What is the length of the diagonal? Round to the nearest hundredth of a foot.

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In the Expanding Your Skills of Section \(8.1,\) we converted U.S. Customary units of area. We use the same procedure to convert metric units of area. This procedure involves multiplying by two unit ratios of length. Example: Converting area Convert \(1000 \mathrm{mm}^{2}\) to square centimeters. $$\text { Solution: } \frac{1000 \mathrm{mm}^{2}}{1} \cdot \frac{1 \mathrm{cm}}{10 \mathrm{mm}} \cdot \frac{1 \mathrm{cm}}{10 \mathrm{mm}}=\frac{1000 \mathrm{mm}^{2}}{1} \cdot \frac{1 \mathrm{cm}^{2}}{100 \mathrm{mm}^{2}}=\frac{1000 \mathrm{cm}^{2}}{100}=10 \mathrm{cm}^{2}$$ convert the units of area, using two factors of the given unit ratio. $$65,000,000 \mathrm{m}^{2}=\quad \mathrm{km}^{2}$$ $$\left(\text { Use } \frac{1 \mathrm{km}}{1000 \mathrm{m}}\right)$$
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