Calculate the final selling price to the nearest cent and markdown percent to the nearest hundredth percent:
| Original selling price | First markdown | Second markdown | Markup | Final markdown |
| :--------------------- | :------------- | :-------------- | :----- | :------------- |
| $6,200 | 35% | 20% | 15% | 5% |
| Final selling price | | | | |
| Markdown percent | % | | | |
Answer (1)
Calculate the price after the first markdown: P 1 = 6200 × ( 1 − 0.35 ) = 4030 .
Calculate the price after the second markdown: P 2 = 4030 × ( 1 − 0.20 ) = 3224 .
Calculate the price after the markup: P 3 = 3224 × ( 1 + 0.15 ) = 3707.60 .
Calculate the final selling price: P 4 = 3707.60 × ( 1 − 0.05 ) = 3522.22 , and the overall markdown percent is 43.19% . The final selling price is $3522.22 .
Explanation
Problem Overview We are given the original selling price of an item and a series of markdowns and a markup. Our goal is to find the final selling price and the overall markdown percentage.
Price After First Markdown First, we calculate the price after the first markdown of 35%: P 1 = 6200 × ( 1 − 0.35 ) = 6200 × 0.65 = 4030 So, the price after the first markdown is $4030.
Price After Second Markdown Next, we calculate the price after the second markdown of 20%: P 2 = 4030 × ( 1 − 0.20 ) = 4030 × 0.80 = 3224 So, the price after the second markdown is $3224.
Price After Markup Then, we calculate the price after the markup of 15%: P 3 = 3224 × ( 1 + 0.15 ) = 3224 × 1.15 = 3707.60 So, the price after the markup is $3707.60.
Final Selling Price Finally, we calculate the price after the final markdown of 5%: P 4 = 3707.60 × ( 1 − 0.05 ) = 3707.60 × 0.95 = 3522.22 So, the final selling price is $3522.22.
Total Markdown Amount Now, we calculate the total markdown amount: M a r k d o w n = 6200 − 3522.22 = 2677.78 The total markdown amount is $2677.78.
Overall Markdown Percentage Finally, we calculate the overall markdown percentage: M a r k d o w n _ p erce n t = 6200 2677.78 × 100 = 43.19 So, the overall markdown percentage is 43.19%.
Final Answer Therefore, the final selling price is $3522.22 and the overall markdown percent is 43.19%.
Examples
Understanding markdowns and markups is crucial in retail. For example, a store might initially mark down an item to attract customers, then apply a small markup to increase profit, and finally offer a final markdown to clear out inventory. Calculating these percentages helps businesses determine the optimal pricing strategy to maximize sales and profitability. This is also useful in personal finance when evaluating sales and discounts to make informed purchasing decisions.
