Problem 25 - Elementary Algebra Within Reach

Question

Find the unit price (in dollars per ounce). A 20 -ounce can of pineapple for \(\$ 0.98\)

Step-by-Step Solution

Answer

The unit price of a 20 -ounce can of pineapple is \$0.049 per ounce.

Step 1: Identify the elements

The total price of the can of pineapple is \$0.98 and the weight of the material in it is 20 ounces.

Step 2: Set the unit price formula

The formula to calculate the unit price is Unit Price = Total Price / Total Weight. The unit price will be in dollars per ounce.

Step 3: Insert the values into the formula and perform the division

Applying the values from Step 1, we get: \(Unit Price = \0.98 / 20 \). Perform the division operation to find the value.

Key Concepts

Division as a Key Concept

Division is one of the fundamental arithmetic operations which is used to distribute a quantity into equal parts. In the context of unit price calculations, division helps us determine how much one unit of a product costs. For instance, to find the unit price of something, like the cost per ounce of a canned good, we divide the total price by the total weight or volume. Let's break this down:

• Identify your total cost. This is your numerator.
• Identify the total quantity of the weight or volume. This is your denominator.

Using division makes it easy to comprehend pricing and help compare costs effectively. By practicing simple division in real-life scenarios, we enhance our understanding of how pricing works. When you next encounter a price per unit problem, remember the goal of dividing: breaking down to find out the worth of each single piece or portion.

Understanding Word Problems

Word problems are real-world problems that require us to apply mathematical concepts to solve them. They typically require a deeper understanding than simple arithmetic problems, as they engage students in reading comprehension and mathematical reasoning. To tackle word problems successfully:

• Read through the problem carefully.
• Identify key information such as total cost and quantity.
• Pay attention to the specific question being asked.

Consider the problem of calculating unit price for a 20-ounce can of pineapple costing $0.98. By carefully picking out the relevant numbers, one can set up the division needed to find the answer. Word problems can initially be challenging, but with practice, they become an excellent way to understand applications of mathematics in everyday situations.

Applying Algebraic Concepts

Algebraic concepts provide a framework for working through practical problems like finding unit prices. Although the exercise appears straightforward, it incorporates key algebraic ideas.When we use the formula for unit price: \[ \text{Unit Price} = \frac{\text{Total Price}}{\text{Total Weight}} \]the process involves:

• Translating a word problem into an algebraic equation.
• Assigning variables if necessary.
• Solving the equation with arithmetic like division.

This mathematical approach empowers students to tackle more complex scenarios by providing a solid foundation in how to manipulate and use equations to find solutions. The ability to transform a real-world problem into mathematical language is a vital skill in mathematics education. Algebraic thinking not only simplifies finding unit prices but also extends to broader problem-solving contexts.