A specific model of computer servers are being sold by Company A for $27,000 each, offering trade discounts of 8% and 5% and by Company B for $35,700 each, offering trade discount rates of 12% and 2%.

a. Which company offers the servers for a cheaper price?

﻿﻿A

﻿﻿B

b. What further trade discount rate must the company with the higher price provide to match the lower price?


Round to two decimal places

To determine which company offers the servers at a cheaper price and what further trade discount rate is required to match the lower price, we need to calculate the net price of the servers after applying the given trade discounts.

### Part a: Calculating Net Prices

#### Company A:
1. Original price: $27,000
2. Trade discounts: 8% and 5%

First, apply the 8% discount:
\[ \text{Price after 8% discount} = 27000 \times (1 - 0.08) = 27000 \times 0.92 = 24840 \]

Next, apply the 5% discount on the new price:
\[ \text{Price after 5% discount} = 24840 \times (1 - 0.05) = 24840 \times 0.95 = 23698 \]

So, the net price from Company A is $23,698.00.

#### Company B:
1. Original price: $35,700
2. Trade discounts: 12% and 2%

First, apply the 12% discount:
\[ \text{Price after 12% discount} = 35700 \times (1 - 0.12) = 35700 \times 0.88 = 31416 \]

Next, apply the 2% discount on the new price:
\[ \text{Price after 2% discount} = 31416 \times (1 - 0.02) = 31416 \times 0.98 = 30787.68 \]

So, the net price from Company B is $30,787.68.

Comparing the net prices:
- Company A: $23,698.00
- Company B: $30,787.68

Therefore, **Company A** offers the servers for a cheaper price.

### Part b: Further Trade Discount Rate Required

We need to find the further trade discount rate $ r $ that Company B must offer to match the price of $23,698.00 from Company A.

Starting with the price after initial discounts from Company B, $30,787.68, we need the price after the additional discount to equal $23,698.00.

Let the new price be $ P $:
\[ P = 30787.68 \times (1 - r) = 23698 \]

Solving for $ r $:
\[ 1 - r = \frac{23698}{30787.68} \]
\[ r = 1 - \frac{23698}{30787.68} \]

\[ r = 1 - 0.7699 \]
\[ r = 0.2301 \]

Converting $ r $ to a percentage:
\[ r \times 100 \% = 23.01 \% \]

So, Company B must provide a further trade discount rate of **23.01%** to match the price offered by Company A.

### Summary:
1. Company A offers the servers at a cheaper price.
2. Company B must provide an additional trade discount of 23.01% to match Company A's price.

Do you have any questions or need further details?

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**Tip:** When working with percentages, always convert them to their decimal form before performing any calculations.

Compare the prices of computer servers from Company A and Company B after trade discounts. Learn how to calculate net prices using percentages and find out how much additional discount Company B needs to match Company A's price.

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