Problem 26 - Thinking Mathematically

Question

A store received 200 containers of juice to be sold by April 1 . Each container cost the store \(\$ 0.75\) and sold for \(\$ 1.25\). The store signed a contract with the manufacturer in which the manufacturer agreed to a \(\$ 0.50\) refund for every container not sold by April 1. If 150 containers were sold by April 1 , how much profit did the store make?

Step-by-Step Solution

Answer

The store made a profit of \$62.50

Step 1: Calculate Total Cost

First, calculate the total cost of the containers by multiplying the number of containers, which is 200, by their individual cost, which is \$0.75. Thus, the formula will be \(200*0.75 = \$150\).

Step 2: Calculate Sold Container Profit

Next, calculate how much was made from the containers that were sold. This can be done by multiplying the number of sold containers (150) by their selling price (\$1.25). The formula is \(150*1.25 = \$187.50\).

Step 3: Calculate Refund Profit

Then, calculate the amount made from refunded containers. This will be done by multiplying the number of refunded containers (200-150=50) by the refund for each container (\$0.50). The formula is \(50*0.50 = \$25\).

Step 4: Calculate Total Profit

Finally, calculate the total profit by adding the amount made from selling and refunding containers and then subtracting the total cost. The formula is \((187.50+25)-150 = \$62.50\).

Key Concepts

Profit and Loss Analysis

Profit and loss analysis is a crucial part of managing a business effectively. It involves examining the difference between the revenue generated from sales and the expenses incurred from acquiring the goods. In the given exercise, the analysis breaks down into clear steps. Firstly, we need to understand that the total income comprises both the revenue from the containers sold by April 1 and the refund from the manufacturer for unsold items. On the other hand, the total expenses are solely the initial cost of purchasing all the containers.

To deepen our understanding, let's consider another scenario. Imagine a bookstore sells novels and also earns a commission for bookmarks left unsold by a certain date. The process remains similar where we calculate the total revenue from novels and add the commission from bookmarks, then subtract the cost of purchasing all inventory to determine the bookstore's profit. Through this consistent approach across various business situations, students can sharpen their analytical skills for various economic scenarios.

Quantitative Reasoning

Quantitative reasoning involves the application of mathematical concepts to solve problems related to quantities. In our exercise, we applied quantitative reasoning to determine how much profit the store made. We identify the given information—cost price, selling price, and refund amount—and systematically apply this to the quantities involved: the number of containers purchased, sold, and unsold.

Building Strong Quantitative Foundations

Through exercises like this, students can enhance their capability to reason quantitatively in everyday contexts. Whether it's budgeting personal finances or analyzing the profitability of a business venture, these foundational skills are invaluable. The ability to translate real-world situations into mathematical problems is the essence of quantitative reasoning.

Basic Arithmetic Operations

Basic arithmetic operations, which include addition, subtraction, multiplication, and division, are the building blocks for more complex mathematical problems. The steps required to solve our store's profit scenario rely on these fundamental operations. The multiplication of cost and selling prices by their respective quantities, addition of different revenue streams, and subtraction of costs from total revenue all showcase the use of basic arithmetic.

These operations aren't just mathematical abstractions; they are tools we use daily. For instance, when splitting a dinner bill, calculating travel expenses, or simply shopping for groceries, we’re applying basic arithmetic without even realizing it.

Economic Transactions in Mathematics

Mathematics is intertwined with economic transactions, often used to analyze and make informed financial decisions. In our exercise, mathematics helped us to reconcile the transactions involving the sale and refund of juice containers. It is a clear example of how arithmetic assists in quantifying business activities.

Application in Real-life Transactions

Imagine a lemonade stand where you need to calculate profits after selling lemonade cups and accounting for the unsold lemons returned to the vendor. This microeconomic transaction involves similar principles as our store's juice sales. By recognizing these economic transactions on a small scale, students can extrapolate such thinking to larger scales involving company finances or even national economies.