Question

after a series discount of 16/24, a gps had a net cost of $204.18. what is the list price? the list price of the gps is $\square$. (round to the nearest cent as needed.)

Explanation:

Step1: Understand discount rates

A series discount of 16/24 means first a 16% discount, then a 24% discount on the remaining price. The complement of a discount rate \( d \) is \( 1 - d \). For the first discount (16%), the complement is \( 1 - 0.16 = 0.84 \). For the second discount (24%), the complement is \( 1 - 0.24 = 0.76 \).

Step2: Calculate net cost factor

The net cost factor (NCF) for series discounts is the product of the complements of each discount rate. So, \( \text{NCF} = 0.84 \times 0.76 \).
Calculating that: \( 0.84 \times 0.76 = 0.6384 \).

Step3: Find list price

The net cost (NC) is related to the list price (LP) by \( \text{NC} = \text{LP} \times \text{NCF} \). We know \( \text{NC} = 204.18 \) and \( \text{NCF} = 0.6384 \), so we solve for \( \text{LP} \): \( \text{LP} = \frac{\text{NC}}{\text{NCF}} = \frac{204.18}{0.6384} \).
Calculating that: \( \frac{204.18}{0.6384} \approx 319.83 \).

Answer:

\( 319.83 \)