- Identify the constant price per unit: 7 dollars per pound.
- Represent the variable quantity of pounds as \(p\).
- Multiply the unit price by the quantity: \(7 \times p\).
- The total cost is \(\boxed{7p}\).
Explanation
- Analyzing the Variables and Relationship
To determine the cost of purchasing chocolate, we start by identifying the known values given in the problem. We are told that the cost of one pound of chocolate is 7 dollars. The quantity of chocolate purchased is represented by the variable \(p\), which stands for the number of pounds. The relationship between the total cost, the unit price, and the total weight is defined by the formula:
Total Cost = (Price per pound) × (Number of pounds).
- Formulating the Expression
Using the information provided, we substitute the values into our formula. The price per pound is 7 dollars, and the number of pounds is \(p\). Therefore, the total cost for \(p\) pounds of chocolate can be written as:
Total Cost = \(7 \times p\) or simply \(7p\).
This expression represents the total cost in dollars as a function of the weight purchased.
Examples
Suppose you are buying ingredients for a batch of chocolate brownies. If you need exactly \(p\) pounds of chocolate and the local market sells it for \(\$7\) per pound, this algebraic expression helps you quickly calculate your total expenditure regardless of how many pounds you decide to buy. By substituting the number of pounds you need into the expression \(7p\), you can easily determine the budget required for your purchase.