Digital Fingers Glovers bought 345 pairs of gloves at $31 per pair. 206 pairs were sold in the first month, at the regular price of $55 per pair. Another 53 pairs were sold in the second month at a "one-third-off" the regular selling price. The remaining gloves were cleared out in the third month at $16.64. The store's overhead is 17% of cost.

**a.** What was the total cost?

Round to the nearest cent

**b.** What were the total sales?

Round to the nearest cent

**c.** What was the effective rate of markup as a percent of cost?

%

Round to two decimal places

**d.** What was the total operating profit or loss on the sale of all of the gloves?

Let's break down the problem step by step and solve each part.

### **Given Information:**

- Digital Fingers Glovers bought 345 pairs of gloves at $31 per pair.
- First month sales: 206 pairs at $55 per pair (regular price).
- Second month sales: 53 pairs at one-third off the regular price.
- Third month sales: Remaining gloves sold at $16.64 per pair.
- Overhead: 17% of cost.

### **a. What was the total cost?**

The total cost of the gloves can be calculated by multiplying the number of pairs bought by the cost per pair:

\[
\text{Total Cost} = 345 \times 31 = 10,695
\]

So, the total cost is **$10,695.00**.

### **b. What were the total sales?**

We will calculate the total sales for each month.

1. **First month sales:**  
   206 pairs sold at $55 per pair.
   \[
   \text{Sales for first month} = 206 \times 55 = 11,330
   \]

2. **Second month sales:**  
   53 pairs sold at one-third off the regular price of $55. The discounted price is:
   \[
   \text{Discounted price} = 55 \times \left(1 - \frac{1}{3}\right) = 55 \times \frac{2}{3} = 36.67
   \]
   Total sales for the second month:
   \[
   \text{Sales for second month} = 53 \times 36.67 = 1,943.51
   \]

3. **Third month sales:**  
   The remaining gloves after the first two months are:
   \[
   \text{Remaining gloves} = 345 - (206 + 53) = 86
   \]
   These 86 pairs are sold at $16.64 per pair:
   \[
   \text{Sales for third month} = 86 \times 16.64 = 1,431.04
   \]

Now, we sum up the total sales:
\[
\text{Total Sales} = 11,330 + 1,943.51 + 1,431.04 = 14,704.55
\]

So, the total sales are **$14,704.55**.

### **c. What was the effective rate of markup as a percent of cost?**

The effective rate of markup is calculated using the formula:
\[
\text{Rate of Markup} = \left(\frac{\text{Total Sales} - \text{Total Cost}}{\text{Total Cost}}\right) \times 100
\]
Substitute the values:
\[
\text{Rate of Markup} = \left(\frac{14,704.55 - 10,695}{10,695}\right) \times 100 = \left(\frac{4,009.55}{10,695}\right) \times 100 = 37.48\%
\]

So, the effective rate of markup is **37.48%**.

### **d. What was the total operating profit or loss on the sale of all of the gloves?**

The operating profit or loss is calculated by subtracting the total cost and the overhead from the total sales. The overhead is 17% of the total cost:
\[
\text{Overhead} = 0.17 \times 10,695 = 1,818.15
\]
Now, subtract the total cost and overhead from the total sales:
\[
\text{Operating Profit or Loss} = 14,704.55 - (10,695 + 1,818.15) = 14,704.55 - 12,513.15 = 2,191.40
\]

So, the total operating profit is **$2,191.40**.

---

### **Summary:**

- **a.** Total cost = $10,695.00
- **b.** Total sales = $14,704.55
- **c.** Effective rate of markup = 37.48%
- **d.** Total operating profit = $2,191.40

Let me know if you'd like more details, or if you have any questions!  
Here are 5 related questions to practice:

1. What is the markup amount in dollars?
2. How would the profit change if the overhead were 20% instead of 17%?
3. What would the total sales be if all pairs were sold at the regular price?
4. How much profit would be lost if the third-month gloves were sold at $10 per pair?
5. What was the overall discount applied in the second month?

**Tip:** Always remember to include overhead costs when calculating profits, especially in real-world business scenarios!

Digital Fingers Glovers bought 345 pairs of gloves at $31 per pair. 206 pairs were sold in the first month, at the regular price of $55 per pair. Another 53 pairs were sold in the second month at 'one-third-off' the regular selling price. The remaining gloves were cleared out in the third month at $16.64. The store's overhead is 17% of cost.

a. What was the total cost?

b. What were the total sales?

c. What was the effective rate of markup as a percent of cost?

d. What was the total operating profit or loss on the sale of all of the gloves?

Learn how to calculate total cost, sales revenue, effective markup percentage, and operating profit for a business scenario involving gloves. This problem involves concepts of cost calculation, sales, and profit determination, suitable for Grades 10-12.

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