a department store purchases logo shirts at a cost of $10 per shirt. they increase the price 100% and put…

a department store purchases logo shirts at a cost of $10 per shirt. they increase the price 100% and put them on the sales floor. every month that a shirt doesnt sell, the store reduces the selling price by 25%. after three monthly reductions, the final shirt from the shipment is sold. there is a 5% sales tax on the selling price. explain the steps for finding the final cost to the customer for that shirt?

a department store purchases logo shirts at a cost of $10 per shirt. they increase the price 100% and put them on the sales floor. every month that a shirt doesnt sell, the store reduces the selling price by 25%. after three monthly reductions, the final shirt from the shipment is sold. there is a 5% sales tax on the selling price. explain the steps for finding the final cost to the customer for that shirt?

Answer

Explanation:

Step1: Calculate initial selling - price

The cost per shirt is $10. A 100% increase means the initial selling - price is $10\times(1 + 100%)=10\times2=$20$.

Step2: Calculate price after first reduction

The store reduces the price by 25% each month. After the first reduction, the price is $20\times(1 - 25%)=20\times0.75=$15$.

Step3: Calculate price after second reduction

After the second reduction, the price is $15\times(1 - 25%)=15\times0.75 = 11.25$.

Step4: Calculate price after third reduction

After the third reduction, the price is $11.25\times(1 - 25%)=11.25\times0.75=$8.4375$.

Step5: Calculate final cost with sales tax

There is a 5% sales tax on the selling price. The final cost to the customer is $8.4375\times(1 + 5%)=8.4375\times1.05=$8.859375\approx$8.86$.

Answer:

First, find the initial selling - price by doubling the cost price ($10\times2 = 20$). Then, successively multiply the price by 0.75 three times to account for the 25% monthly reductions ($20\times0.75\times0.75\times0.75 = 8.4375$). Finally, multiply the reduced price by 1.05 to add the 5% sales tax ($8.4375\times1.05\approx8.86$). The final cost to the customer is approximately $$8.86$.