Question

an appliance has a list price of $27.57 and is offered to wholesalers with a series discount of 15/10/5. a retailer is offered the same appliance with a series discount of 15/10. find the difference between the wholesalers price and the retailer’s price. the difference between the two prices is $\square$. (round the final answer to the nearest cent as needed. round all intermediate values to the nearest cent as needed.)

Explanation:

Step1: Calculate wholesaler's price

First, for a series discount of \(15/10/5\), we calculate the net price factor. The formula for net price factor with series discounts is \((1 - d_1)(1 - d_2)(1 - d_3)\), where \(d_1 = 0.15\), \(d_2 = 0.10\), \(d_3 = 0.05\).
\((1 - 0.15)(1 - 0.10)(1 - 0.05)=0.85\times0.90\times0.95\)
\(0.85\times0.90 = 0.765\), then \(0.765\times0.95 = 0.72675\)
Wholesaler's price \(= 27.57\times0.72675\approx27.57\times0.7268\approx19.94\) (rounded to nearest cent)

Step2: Calculate retailer's price

For a series discount of \(15/10\), the net price factor is \((1 - 0.15)(1 - 0.10)=0.85\times0.90 = 0.765\)
Retailer's price \(= 27.57\times0.765\approx21.09\) (rounded to nearest cent)

Step3: Find the difference

Difference \(= 21.09 - 19.94 = 1.15\)

Answer:

\(1.15\)