Problem 93 - Intermediate Algebra

Question

Answer the question with an algebraic expression. The cost of a 5-pound box of candy is \(c\) cents. What is the price per pound?

Step-by-Step Solution

Answer

\(\frac{c}{5}\) cents per pound

Step 1: Identify the Total Cost

The total cost for a 5-pound box of candy is given as \(c\) cents.

Step 2: Understand the Quantity

The total weight of the candy box is 5 pounds.

Step 3: Calculate Price Per Pound

To find the price per one pound of candy, divide the total cost \(c\) by the total number of pounds, which is 5. Thus, the price per pound is \(\frac{c}{5}\) cents.

Key Concepts

Price Calculation

In order to determine the price of a product, we need to understand the relationship between the total cost and the quantity of the product. Here, the total cost of the candy box is represented by the algebraic expression \( c \) for a 5-pound box. To find the cost of a smaller unit, like per pound, we divide the total cost by the number of pounds. This basic method is called unit pricing. It helps buyers compare costs and make informed decisions. Always remember this formula:

• Total Cost / Quantity = Unit Price

By dividing the total cents by the number of pounds, you get the cost for one pound of candy.

Division in Algebra

When dealing with algebraic expressions, division is used to breakdown a total quantity into smaller, manageable parts. Here, the algebraic expression \( \frac{c}{5} \) shows how to distribute the total cost \( c \) evenly across the 5 pounds of candy. In algebra, division can simplify calculations and express relationships between quantities. Keep in mind:

• The numerator indicates what is being divided (the total cost \( c \)).
• The denominator is how many parts we are dividing into (the 5 pounds).

So, the expression \( \frac{c}{5} \) represents a balanced division of costs, providing a clear view of how much each pound costs.

Units of Measurement

Understanding units is crucial when calculating prices. Here, the problem uses pounds to measure weight and cents to measure cost. Units of measurement allow us to work with real-world quantities in an organized way.
When performing calculations:

• Ensure all measurements are in the same system (e.g., pounds for weight and cents for price).
• Convert units if necessary to ensure consistency across calculations.

In this exercise, staying consistent with units allows the division to make sense and ensures the resulting price per pound \( \frac{c}{5} \) is accurate and useful for making cost comparisons.