Calculate the final selling price to the nearest cent and markdown percent to the nearest hundredth percent:
| Original selling price $6,200 | First markdown | Second markdown | Markup | Final markdown |
|---|---|---|---|---|
| | 35% | 20% | | 5% |
| Final selling price | | | | |
| Markdown percent | % | | | |
Answer (1)
Calculate the price after the first markdown: P r i c e 1 = $6200 × ( 1 − 0.35 ) = $4030
Calculate the price after the second markdown: P r i c e 2 = $4030 × ( 1 − 0.20 ) = $3224
Calculate the final selling price: F ina l S e ll in g P r i ce = $3224 × ( 1 − 0.05 ) = $3062.80
Calculate the overall markdown percentage: M a r k d o w n P erce n t a g e = $6200 $6200 − $3062.80 × 100 = 50.60%
The final selling price is $3062.80 and the markdown percentage is 50.60% .
Explanation
Understanding the Problem We are given the original selling price of an item and a series of markdowns. We need to calculate the final selling price and the overall markdown percentage.
Calculating Price After First Markdown First, we calculate the selling price after the first markdown of 35%: P r i c e 1 = O r i g ina l P r i ce × ( 1 − F i rs t M a r k d o w n P erce n t a g e ) P r i c e 1 = $6200 × ( 1 − 0.35 ) P r i c e 1 = $6200 × 0.65 P r i c e 1 = $4030
Calculating Price After Second Markdown Next, we calculate the selling price after the second markdown of 20%: P r i c e 2 = P r i c e 1 × ( 1 − S eco n d M a r k d o w n P erce n t a g e ) P r i c e 2 = $4030 × ( 1 − 0.20 ) P r i c e 2 = $4030 × 0.80 P r i c e 2 = $3224
Calculating Final Selling Price Then, we calculate the final selling price after the final markdown of 5%: F ina l S e ll in g P r i ce = P r i c e 2 × ( 1 − F ina l M a r k d o w n P erce n t a g e ) F ina l S e ll in g P r i ce = $3224 × ( 1 − 0.05 ) F ina l S e ll in g P r i ce = $3224 × 0.95 F ina l S e ll in g P r i ce = $3062.80
Calculating Total Markdown Amount Now, we calculate the total markdown amount: T o t a l M a r k d o w n = O r i g ina l P r i ce − F ina l S e ll in g P r i ce T o t a l M a r k d o w n = $6200 − $3062.80 T o t a l M a r k d o w n = $3137.20
Calculating Overall Markdown Percentage Finally, we calculate the overall markdown percentage: M a r k d o w n P erce n t a g e = O r i g ina l P r i ce T o t a l M a r k d o w n × 100 M a r k d o w n P erce n t a g e = $6200 $3137.20 × 100 M a r k d o w n P erce n t a g e = 0.506 × 100 M a r k d o w n P erce n t a g e = 50.60%
Final Answer The final selling price is $3062.80, and the overall markdown percentage is 50.60%.
Examples
Understanding markdowns is crucial in retail. Imagine a store needs to clear out seasonal inventory. By applying a series of markdowns, like the ones in this problem, the store can attract customers with lower prices while still making some profit. Calculating these markdowns accurately helps the store manage its inventory and pricing strategy effectively. For example, a clothing store might initially mark down summer clothes by 35% in August, then another 20% in September, and a final 5% in October to clear out the remaining stock.
