Digital Fingers Glovers bought 358 pairs of gloves at $26 per pair. 218 pairs were sold in the first month, at the regular price of $44 per pair. Another 47 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 $17.73. The store's overhead is 16% of cost.What was the effective rate of markup as a percent of cost?

We can break down the problem step-by-step to calculate the effective rate of markup as a percent of cost.

### Step 1: Total Cost of the Gloves
The total cost of the gloves is calculated by multiplying the number of pairs bought by the cost per pair.

\[
\text{Total Cost} = 358 \times 26 = 9,308 \, \text{dollars}
\]

### Step 2: Revenue from Sales
We will calculate the revenue generated from selling the gloves over three months.

#### First Month:
218 pairs were sold at $44 per pair.

\[
\text{Revenue (First Month)} = 218 \times 44 = 9,592 \, \text{dollars}
\]

#### Second Month:
47 pairs were sold at a "one-third-off" discount. So, the price per pair was reduced by one-third:

\[
\text{Discounted Price} = 44 \times \left(1 - \frac{1}{3}\right) = 44 \times \frac{2}{3} = 29.33
\]

\[
\text{Revenue (Second Month)} = 47 \times 29.33 = 1,379.51 \, \text{dollars}
\]

#### Third Month:
The remaining number of gloves, which is $358 - 218 - 47 = 93$, were sold at $17.73 per pair.

\[
\text{Revenue (Third Month)} = 93 \times 17.73 = 1,648.89 \, \text{dollars}
\]

### Step 3: Total Revenue
Now, we can calculate the total revenue from all three months.

\[
\text{Total Revenue} = 9,592 + 1,379.51 + 1,648.89 = 12,620.40 \, \text{dollars}
\]

### Step 4: Total Overhead Costs
The store's overhead is 16% of the total cost.

\[
\text{Overhead} = 0.16 \times 9,308 = 1,489.28 \, \text{dollars}
\]

### Step 5: Net Profit
The net profit is the total revenue minus the total cost and the overhead.

\[
\text{Net Profit} = 12,620.40 - 9,308 - 1,489.28 = 1,823.12 \, \text{dollars}
\]

### Step 6: Effective Markup as a Percentage of Cost
Finally, the effective rate of markup as a percentage of the total cost is calculated as:

\[
\text{Markup Percentage} = \left(\frac{\text{Net Profit}}{\text{Total Cost}}\right) \times 100 = \left(\frac{1,823.12}{9,308}\right) \times 100 = 19.59\%
\]

Thus, the **effective rate of markup** as a percent of cost is approximately **19.59%**.

Would you like more details or have any questions?

### Related Questions:
1. How would the effective markup change if overhead increased to 20%?
2. What would the new markup rate be if the third month's price was $20 instead of $17.73?
3. How much profit would Digital Fingers Glovers make if they sold all pairs in the first month at $44 per pair?
4. What is the break-even price for each glove pair if overhead is considered?
5. How does the total revenue compare if the gloves were sold at $30 per pair in the second month?

**Tip**: To maximize profits, it’s essential to strike a balance between discounting and maintaining a price that covers overhead.

Digital Fingers Glovers bought 358 pairs of gloves at $26 per pair. 218 pairs were sold in the first month, at the regular price of $44 per pair. Another 47 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 $17.73. The store's overhead is 16% of cost. What was the effective rate of markup as a percent of cost?

Learn how to calculate the effective markup percentage on a purchase of 358 pairs of gloves sold over three months with varying prices and a 16% overhead cost. This detailed problem involves percentage calculations, profit analysis, and pricing strategies. Suitable for students in Grades 10-12.

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