A catering company buys some items with a list price of $$ \$ 3,000 $$. If the supplier extends trade discount rates of $$ 45 / 30 / 5 $$, find the net price using the net price factor, complement method.

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To determine the **net price** after applying the trade discounts of $$45\%$$, $$30\%$$, and $$5\%$$ using the **net price factor (complement method)**, follow these steps:

### Step 1: Calculate the Net Price Factor

The net price factor is found by taking the complement of each discount rate and multiplying them together:

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

Where:
- $$d_1 = 45\% = 0.45$$
- $$d_2 = 30\% = 0.30$$
- $$d_3 = 5\% = 0.05$$

$$
\text{Net Price Factor} = (1 - 0.45) \times (1 - 0.30) \times (1 - 0.05) = 0.55 \times 0.70 \times 0.95
$$

$$
\text{Net Price Factor} = 0.55 \times 0.70 = 0.385
$$
$$
\text{Net Price Factor} = 0.385 \times 0.95 = 0.36575
$$

### Step 2: Calculate the Net Price

Multiply the net price factor by the list price:

$$
\text{Net Price} = \text{List Price} \times \text{Net Price Factor} = \$3,000 \times 0.36575 = \$1,097.25
$$

### Final Answer

The net price after applying the trade discounts is **\$1,097.25**.
The net price after applying the trade discounts is \$1,097.25.

A catering company buys some items with a list price of \( \$ 3,000 \). If the supplier extends trade discount rates of \( 45 / 30 / 5 \), find the net price using the net price factor, complement method.

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