Problem 21 - Thinking Mathematically

Question

Each day a small business owner sells 200 pizza slices at \(\$ 1.50\) per slice and 85 sandwiches at \(\$ 2.50\) each. If business expenses come to \(\$ 60\) per day, what is the owner's profit for a 10 -day period?

Step-by-Step Solution

Answer

The owner's profit for a 10-day period is \(\$4525\).

Step 1: Compute Daily Income

First, the daily income needs to be calculated. This is done by multiplying the number of each type of product sold by its price. The number of pizza slices sold each day is 200, and each slice costs \(\$1.50\). So, the income from the pizza slices per day is 200*\(1.50\)=\(\$300\). Similarly, the number of sandwiches sold each day is 85, and each sandwich costs \(\$2.50\). So, the income from the sandwiches each day is 85*\(2.50\)=\(\$212.50\). Thus, the total daily income is \(\$300\) + \(\$212.50\) = \(\$512.50\).

Step 2: Calculate Daily Profit

The daily expenses amount to \(\$60\). The profit each day can be calculated by subtracting the daily expenses from the daily income: \(\$512.50\) - \(\$60\) = \(\$452.50\). This is the profit each day.

Step 3: Find Total Profit for a 10-day period

To calculate the total profit for a 10-day period, the daily profit should be multiplied by the number of days. So, \(\$452.50\) * 10 = \(\$4525\) is the total profit for a 10-day period.

Key Concepts

Daily Income

Understanding daily income is crucial for running a successful business. In this context, daily income refers to the money received from selling goods each day. To calculate the daily income, multiply the number of items sold by their respective prices.
For example:

• For pizza slices, if you sell 200 each day at \(1.50 each, your income from pizza slices would be: \(200 \times 1.50 = \\)300\).
• For sandwiches, if you sell 85 each day at \(2.50 each, your income from sandwiches would be: \(85 \times 2.50 = \\)212.50\).

By adding these values together, you have the total daily income: \(300 + 212.50 = \$512.50\).
This calculation helps business owners know how much money they can expect to bring in each day from their sales.

Business Expenses

Business expenses are the costs associated with running a business. Understanding and managing these expenses is vital to profitability. Expenses can include rent, utilities, or other daily operational costs.
For our example:

• The daily expenses are given as \(\\(60\).

Once you know your income, subtract the expenses to find the daily profit. Expense management ensures businesses set aside enough funds to cover these costs while maximizing the remaining revenue as profit. For instance, using our income from above, the daily profit calculation would be:\(512.50 - 60 = \\)452.50\).

Pizza Slices

The number of pizza slices sold and their pricing play a significant role in calculating business income. By focusing on this part of the sales, you can better understand how much revenue they contribute.
Remember to consider:

• The price per slice, which is \(\\(1.50\) in our scenario.
• The quantity sold daily, here it's 200 slices.

Calculating the pizza revenue involves multiplying the price by the amount sold:\(200 \times 1.50 = \\)300\).
This figure is crucial for assessing how much of the daily income comes from pizza slices and helps in strategizing for potential increases in sales for higher profits.

Sandwiches

Sandwiches, like pizza slices, play a critical role in determining the overall daily income. It’s essential to understand their contribution to the business's revenue.
Here's what to consider:

• Each sandwich is sold for \(\\(2.50\).
• The business sells 85 sandwiches daily.

To calculate income from sandwiches, multiply the number sold by the price per item:\(85 \times 2.50 = \\)212.50\).
Knowing how much sandwiches contribute to the daily income helps in making informed decisions about pricing and marketing efforts. This understanding is part of maintaining a balanced menu that appeals to customers and ensures healthy profit margins.