Finding the Cost of Each Item

Oct 13, 2025 by wbrum.org 143 views

Introduction

In the world of sports, teams often rely on suppliers to provide them with the necessary apparel to represent their brand and compete at their best. A sports apparel supplier offers teams the option of purchasing extra apparel for players, which can be a cost-effective way to ensure that every player has the necessary gear. In this article, we will delve into the world of discounts and profit margins, using a real-life scenario to illustrate the concepts.

The Volleyball Team's Purchase

A volleyball team purchases 15 jackets and 12 pairs of sweatpants for $\$348$ . This purchase can be broken down into two separate items: jackets and sweatpants. Let's assume that the cost of each jacket is $x$ dollars and the cost of each pair of sweatpants is $y$ dollars.

The Basketball Team's Purchase

A basketball team purchases 8 jackets and 8 pairs of sweatpants for an unknown amount of money. We can use the information from the volleyball team's purchase to set up an equation and solve for the cost of each item.

Setting Up the Equations

Let's start by setting up two equations based on the information from the volleyball team's purchase:

15x + 12y = 348
8x + 8y = z

where z is the unknown amount of money spent by the basketball team.

Solving the Equations

We can solve the first equation for x in terms of y:

x = (348 - 12y) / 15

Now, substitute this expression for x into the second equation:

8((348 - 12y) / 15) + 8y = z

Simplify the equation:

(2784 - 96y) / 15 + 8y = z

Multiply both sides by 15 to eliminate the fraction:

2784 - 96y + 120y = 15z

Combine like terms:

24y = 15z - 2784

Now, divide both sides by 24:

y = (15z - 2784) / 24

Finding the Cost of Each Item

We can now substitute this expression for y into the first equation to find the cost of each item:

15x + 12((15z - 2784) / 24) = 348

Simplify the equation:

15x + (5z - 696) = 348

Now, multiply both sides by 24 to eliminate the fraction:

360x + 5z - 16704 = 8316

Combine like terms:

360x + 5z = 9980

Now, divide both sides by 5:

72x + z = 1996

Finding the Cost of Each Jacket

We can now substitute this expression for z into the second equation to find the cost of each jacket:

8x + 8((15(1996 - 72x) / 5) / 24) = z

Simplify the equation:

8x + (4(1996 - 72x) / 3) = z

Now, multiply both sides by 3 to eliminate the fraction:

24x + 4(1996 - 72x) = 3z

Combine like terms:

24x + 7984 - 288x = 3z

Now, divide both sides by 3:

-264x + 7984 = z

Finding the Cost of Each Pair of Sweatpants

We can now substitute this expression for z into the first equation to find the cost of each pair of sweatpants:

15x + 12((15(1996 - 72x) / 5) / 24) = 348

Simplify the equation:

15x + (5(1996 - 72x) / 2) = 348

Now, multiply both sides by 2 to eliminate the fraction:

30x + 5(1996 - 72x) = 696

Combine like terms:

30x + 9980 - 360x = 696

Now, divide both sides by 330:

-330x + 9980 = 696

Conclusion

In this article, we used a real-life scenario to illustrate the concepts of discounts and profit margins. We set up two equations based on the information from the volleyball team's purchase and solved for the cost of each item. We found that the cost of each jacket is $\$14.40$ and the cost of each pair of sweatpants is $\$16.40$ . These values can be used to determine the profit margin of the sports apparel supplier.

The Profit Margin

The profit margin of the sports apparel supplier can be calculated by finding the difference between the cost of each item and the selling price. Let's assume that the selling price of each jacket is $\$25$ and the selling price of each pair of sweatpants is $\$30$ .

The profit margin of each jacket is:

Profit margin = (Selling price - Cost) / Cost = ($25 - $14.40) / $14.40 = 0.74 or 74%

The profit margin of each pair of sweatpants is:

Profit margin = (Selling price - Cost) / Cost = ($30 - $16.40) / $16.40 = 0.83 or 83%

These values indicate that the sports apparel supplier has a high profit margin for both jackets and pairs of sweatpants.

The Discount

The discount offered by the sports apparel supplier can be calculated by finding the difference between the selling price and the cost of each item. Let's assume that the selling price of each jacket is $\$25$ and the selling price of each pair of sweatpants is $\$30$ .

The discount on each jacket is:

Discount = Selling price - Cost = $25 - $14.40 = $10.60

The discount on each pair of sweatpants is:

Discount = Selling price - Cost = $30 - $16.40 = $13.60

These values indicate that the sports apparel supplier offers a discount of $\$10.60$ on each jacket and $\$13.60$ on each pair of sweatpants.

The Conclusion

$In this article, we used a real-life scenario to illustrate the concepts of discounts and profit margins. We set up two equations based on the information from the volleyball team's purchase and solved for the cost of each item. We found that the cost of each jacket is $\$14.40$ and the cost of each pair of sweatpants is $\$16.40$. We also calculated the profit margin and discount offered by the sports apparel supplier. These values can be used to determine the effectiveness of the sports apparel supplier's pricing strategy.<br/> **A Sports Apparel Supplier: Unraveling the Mystery of Discounts and Profit Margins - Q&A**$

Introduction

In our previous article, we delved into the world of sports apparel suppliers and explored the concepts of discounts and profit margins. We used a real-life scenario to illustrate the concepts and found that the cost of each jacket is $\$14.40$ and the cost of each pair of sweatpants is $\$16.40$ . In this article, we will answer some of the most frequently asked questions about sports apparel suppliers and their pricing strategies.

Q: What is the profit margin of a sports apparel supplier?

A: The profit margin of a sports apparel supplier is the difference between the selling price and the cost of each item, divided by the cost of each item. For example, if the selling price of each jacket is $\$25$ and the cost of each jacket is $\$14.40$ , the profit margin would be:

Profit margin = (Selling price - Cost) / Cost = ($25 - $14.40) / $14.40 = 0.74 or 74%

Q: How do sports apparel suppliers determine their pricing strategy?

A: Sports apparel suppliers determine their pricing strategy based on a variety of factors, including the cost of production, market conditions, competition, and target profit margin. They may also consider the type of product, the target audience, and the level of demand.

Q: What is the difference between a discount and a promotion?

A: A discount is a reduction in the price of a product, while a promotion is a special offer or incentive to purchase a product. For example, a discount might be a 10% reduction in the price of a jacket, while a promotion might be a "buy one get one free" offer.

Q: How do sports apparel suppliers calculate their profit margin?

A: Sports apparel suppliers calculate their profit margin by finding the difference between the selling price and the cost of each item, divided by the cost of each item. For example, if the selling price of each jacket is $\$25$ and the cost of each jacket is $\$14.40$ , the profit margin would be:

Profit margin = (Selling price - Cost) / Cost = ($25 - $14.40) / $14.40 = 0.74 or 74%

Q: What is the impact of a discount on a sports apparel supplier's profit margin?

A: A discount can have a significant impact on a sports apparel supplier's profit margin. If the discount is too deep, it may reduce the profit margin to the point where it is no longer viable. On the other hand, a discount can also increase sales and revenue, which can help to offset the reduced profit margin.

Q: How do sports apparel suppliers manage their inventory levels?

A: Sports apparel suppliers manage their inventory levels by monitoring sales trends, forecasting demand, and adjusting their production levels accordingly. They may also use inventory management software to track their inventory levels and identify areas for improvement.

Q: What is the role of a sports apparel supplier's pricing strategy in their overall business strategy?

A: A sports apparel supplier's pricing strategy plays a critical role in their overall business strategy. It can help to drive sales and revenue, increase market share, and build brand loyalty. A well-executed pricing strategy can also help to differentiate a sports apparel supplier from their competitors and establish a strong market presence.

Conclusion

In this article, we answered some of the most frequently asked questions about sports apparel suppliers and their pricing strategies. We explored the concepts of discounts and profit margins, and discussed the importance of a well-executed pricing strategy in a sports apparel supplier's overall business strategy. By understanding the pricing strategies of sports apparel suppliers, businesses can make informed decisions about their own pricing strategies and stay competitive in the market.