Problem 34 - Algebra for College Students

Question

Solve each equation. The owner of a pizza parlor wants to make a profit of \(70 \%\) of the cost for each pizza sold. If it costs \(\$ 2.50\) to make a pizza, at what price should each pizza be sold?

Step-by-Step Solution

Answer

The pizza should be sold for $4.25.

Step 1: Understanding the Problem

First, we need to determine the total price at which the pizza should be sold to achieve a 70% profit over the cost of making one pizza. The cost of making a pizza is $2.50.

Step 2: Calculating the Profit Amount

To find the profit, we calculate 70% of the cost of making a pizza. This is done by multiplying the cost of the pizza by 0.70: \[ \text{Profit} = 0.70 \times 2.50 \] Calculating this gives:\[ \text{Profit} = 1.75 \]

Step 3: Determining the Selling Price

To determine the selling price, we add the profit to the cost of making the pizza:\[ \text{Selling Price} = \text{Cost} + \text{Profit} = 2.50 + 1.75 \] This results in:\[ \text{Selling Price} = 4.25 \]

Step 4: Conclusion

Therefore, the pizza should be sold for $4.25 to make a 70% profit over cost.

Key Concepts

Percentage Calculation

Percentage calculation is a crucial skill in algebra that involves finding a portion of a whole number. In the context of our exercise, we are dealing with finding a percentage of the cost to determine the profit. When you want to calculate a percentage, you multiply the total by the desired percentage expressed as a decimal.
For instance, if the cost to produce a pizza is $2.50 and we wish to find 70% of this cost, we convert 70% to a decimal by dividing by 100, yielding 0.70. Therefore, the calculation becomes: \( 0.70 \times 2.50 = 1.75 \).

• To find the decimal equivalent of a percentage, divide by 100.
• Multiply the original number by this decimal to get the percentage amount.

Understanding this process helps break down complex algebra problems into simple steps.

Profit and Loss

Profit and loss concepts are central to business mathematics, especially in transactions involving buying and selling. The profit is the amount by which the revenue of a sale exceeds the cost.
In our example, the pizza parlor owner wants a profit of 70% over the $2.50 cost of each pizza. We found that this profit translates to $1.75.

• Profit is calculated by multiplying the cost by the profit percentage in decimal form.
• The selling price is the sum of the original cost and the profit.

So, understanding profit and loss involves not just calculating percentages but also applying them to real-world financial decisions.

Problem Solving Strategies

In tackling algebra problems, employing effective problem solving strategies is vital. This involves understanding the problem, devising a plan, performing the calculations, and checking your work.
Let's recap the steps we took to solve the problem of setting the pizza's selling price:

• Clearly understand what the question is asking: Determine the selling price with a 70% profit.
• Set up a plan: Calculate the profit and add it to the costs.
• Execute the calculations: We calculated the 70% of $2.50, then added this to the initial cost.
• Verify the result: Ensure that $4.25 indeed represents a price that covers cost plus profit.

Thus, breaking down the problem and organizing the approach helps in reaching the correct solution efficiently.