To solve these problems, we need to find both the original list price of the printer and the single equivalent trade discount rate for the series of discounts Marissa received.

Part a: Finding the List Price

Let the list price be $P$. Marissa received discounts of 12%, 3%, and 3% sequentially. To find the net price after each discount, we can use the following formula:

$\text{Net Price} = P \times (1 - d_1) \times (1 - d_2) \times (1 - d_3)$

where $d_1 = 0.12$, $d_2 = 0.03$, and $d_3 = 0.03$.

Given that the net price after the discounts is $350.61, we can set up the equation:

$350.61 = P \times (1 - 0.12) \times (1 - 0.03) \times (1 - 0.03)$

Calculate the combined discount factor:

$350.61 = P \times 0.88 \times 0.97 \times 0.97$

$350.61 = P \times 0.825624$

Now, solve for $P$:

$P = \frac{350.61}{0.825624}$

$P \approx 424.65$

So, the list price of the printer is approximately $424.65.

Part b: Finding the Equivalent Trade Discount Rate

To find the single equivalent trade discount rate, we need to determine the total discount factor from the series of discounts and then convert it back to a percentage.

The total discount factor is:

$(1 - 0.12) \times (1 - 0.03) \times (1 - 0.03) = 0.88 \times 0.97 \times 0.97$

Calculate this product:

$0.88 \times 0.97 \times 0.97 = 0.825624$

The equivalent trade discount rate $D$ is:

$D = 1 - 0.825624$

$D \approx 0.174376$

Convert this to a percentage:

$D \approx 17.44\%$

So, the single equivalent trade discount rate is approximately 17.44%.

Summary

a. The list price of the printer is approximately $424.65.

b. The single equivalent trade discount rate is approximately 17.44%.

Would you like more details or have any questions?

Here are 8 related questions to expand your understanding:

1. How would the list price change if the first discount was 15% instead of 12%?
2. What is the net price if only a single discount of 17.44% was applied to the list price of $424.65?
3. How would you calculate the list price if Marissa had received different discounts of 10%, 5%, and 2%?
4. What is the formula for calculating the equivalent trade discount rate for any series of discounts?
5. How does the order of applying discounts affect the final price?
6. If another item had a list price of $500 and the same series of discounts were applied, what would be the net price?
7. How can you use a spreadsheet to calculate net prices and equivalent discount rates efficiently?
8. What is the impact of rounding intermediate values in the calculations on the final results?

Tip: When dealing with multiple trade discounts, always multiply the complements of the discounts (i.e., $1 - \text{discount}$) to find the combined effect, rather than adding the discounts directly.