Par Putters Company sells golf balls for ​$32 per dozen. The​ store's overhead expenses are 34​% of cost and the owners require a profit of 24​% of cost.
​(a) For how much does Par Putters Company buy one dozen golf​ balls?
​(b) What is the price needed to cover all of the costs and​ expenses?
​(c) What is the highest rate of markdown at which the store will still break​ even?
​(d) What is the highest rate of discount that can be advertised without incurring an absolute​ loss?

Let's break down each part of the question systematically.

### (a) For how much does Par Putters Company buy one dozen golf balls?
- Let the cost price of one dozen golf balls be $ C $.
- The store sells golf balls for $32 per dozen, and this price includes overhead expenses and profit.

We are given:
- Overhead expenses are 34% of the cost price.
- Profit is 24% of the cost price.

Thus, the total selling price is made up of:
- The cost price $ C $,
- Plus 34% of $ C $ for overhead expenses,
- Plus 24% of $ C $ for profit.

This means the selling price $ S $ is:
\[
S = C + 0.34C + 0.24C
\]
\[
S = 1.58C
\]
We know the selling price is $32, so:
\[
32 = 1.58C
\]
Solving for $ C $:
\[
C = \frac{32}{1.58} \approx 20.25
\]
So, Par Putters Company buys one dozen golf balls for approximately **$20.25**.

### (b) What is the price needed to cover all of the costs and expenses?
To cover all the costs and expenses, the company needs to cover the cost price $ C $ and the overhead expenses of 34% of $ C $.

Thus, the price to cover all costs and expenses is:
\[
\text{Price to cover costs and expenses} = C + 0.34C = 1.34C
\]
Substitute $ C = 20.25 $:
\[
\text{Price to cover costs and expenses} = 1.34 \times 20.25 \approx 27.14
\]
So, the price needed to cover all costs and expenses is approximately **$27.14**.

### (c) What is the highest rate of markdown at which the store will still break even?
The store will break even when it sells the golf balls for the amount that covers all costs and expenses. This is the price calculated in part (b), $27.14.

The highest markdown from the original selling price $ S = 32 $ at which the store will break even is:
\[
\text{Markdown} = \frac{S - \text{break-even price}}{S} \times 100
\]
\[
\text{Markdown} = \frac{32 - 27.14}{32} \times 100 \approx 15.19\%
\]
So, the highest rate of markdown for the store to still break even is approximately **15.19%**.

### (d) What is the highest rate of discount that can be advertised without incurring an absolute loss?
The highest rate of discount that can be advertised without incurring a loss is the percentage that will reduce the selling price to the cost price $ C $, because selling below the cost price would result in a loss.

Thus, the highest discount is calculated as:
\[
\text{Discount} = \frac{S - C}{S} \times 100
\]
\[
\text{Discount} = \frac{32 - 20.25}{32} \times 100 \approx 36.72\%
\]
So, the highest rate of discount that can be advertised without incurring a loss is approximately **36.72%**.

---

Would you like more details on any of the calculations or further clarifications?

### Follow-up Questions:
1. How would the profit percentage change if the selling price increased to $35 per dozen?
2. What would be the new overhead expenses if they were 40% of the cost instead of 34%?
3. If the company wanted to make a 30% profit, how much should the new selling price be?
4. How does the selling price affect the markdown percentage allowed for the company to break even?
5. What is the effect of increasing the profit margin on the break-even price?

### Tip:
Always remember that overhead expenses and profit are typically calculated based on the cost price, not the selling price.

Par Putters Company sells golf balls for ​$32 per dozen. The​ store's overhead expenses are 34​% of cost and the owners require a profit of 24​% of cost. (a) For how much does Par Putters Company buy one dozen golf​ balls? (b) What is the price needed to cover all of the costs and​ expenses? (c) What is the highest rate of markdown at which the store will still break​ even? (d) What is the highest rate of discount that can be advertised without incurring an absolute​ loss?

Find out how Par Putters Company calculates the cost price of golf balls, necessary pricing to cover costs, and the highest markdown and discount rates. Learn step-by-step solutions using profit and loss formulas and percentage calculations. Suitable for high school students (Grades 10-12).

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation