Problem 13 - Algebra 1

Question

Find the unit rate. \(\$ 1.39\) for \(1 \frac{1}{2}\) quarts of juice

Step-by-Step Solution

Answer

The unit rate is approximately \$0.93 per quart.

Step 1: Identify the Given Rate

In the problem, the given rate is \$1.39 for 1.5 quarts of juice.

Step 2: Convert to a Unit Rate

A unit rate is a rate with 1 in the denominator. To find the unit rate, divide the cost (\$1.39) by the number of quarts (1.5). Use a calculator to find the quotient: \$1.39 ÷ 1.5 = \$0.93 (to two decimal places).

Step 3: State the Result

Therefore, the unit rate, or the cost of the juice per quart, is approximately \$0.93.

Key Concepts

Rate Calculation

Imagine you're at a store and you find a deal that offers some amount of juice for a particular price, like in our example: $1.39 for 1.5 quarts of juice. A rate compares two related quantities. Here, it's the price ($1.39) per quantity (1.5 quarts of juice).

To calculate it, identify the total cost and total quantity involved. It's always handy to express the price of a single unit of the product to easily compare it with other products. The core idea of rate calculation is to figure out how much one unit of something costs or what the rate per unit is. Simply put:

• Identify the total amount of money, in this case, $1.39.
• Identify the total quantity, which is 1.5 quarts of juice.
• To find the rate, we'll simplify or adjust these numbers, often preparing for division.

Once you've done this preparation, you're ready for the next step: division.

Division

Division is the mathematical process we use to calculate how much one unit costs in our given problem. When you see a fraction like 1.5, or numbers that need to be divided such as 1.39 divided by 1.5, we're using division to break down the information into simpler, digestible parts.

Here's how to do it: we divide the total cost of the juice, $1.39, by the total quantity of juice, which is 1.5 quarts. This operation will tell us the cost per single quart. It's important to use a calculator for precise results if the numbers don't divide evenly.

• Divide $1.39 by 1.5.
• You get approximately $0.93; that's the rate per quart.

Division helps to simplify rates to a per-unit basis. This allows comparisons or assessments to be made more easily when choosing amongst different options or prices. It's all about making complex data easy to understand.

Unit Conversion

Unit conversion is often necessary when dealing with real-world applications like this. Sometimes, quantities can be expressed in inconvenient units that require conversion. For instance, converting 1.5 quarts into another measurement like liters or just simplifying rates to a common unit basis can be crucial.

In our example, no complex unit conversion is needed beyond simplifying to a single quart. This problem is solved solely with basic units provided in the question: dollars and quarts. Yet, knowing how to convert between units—should it be needed—is invaluable:

• Understand what unit conversion applies, e.g., quarts to liters.
• Use conversion factors when necessary. (For instance, 1 liter ≈ 1.0567 quarts)
• Set up conversion equations if other units are presented.

You won't need conversion for this particular problem since it's asking for a unit rate directly in quarts, but the skill of unit conversion ensures a well-rounded problem-solving approach.