A company offers a series of products for sale which pay different rates of commission to the salesperson. Platinum products pay a 20 percent commission. Gold products pay a 15 percent commission. Silver products pay 10 percent and Bronze products pay 5 percent. How much would a salesperson need to sell in Platinum products in order to equal the total commissions earned from a combined sale of $1,000 in Gold products and $15,000 in Bronze products? 1) $11,250 2) $900 3) $3,600 4) $4,500

4) $4,500

Explanation:

According to given data

Commission rates

Platinum products = 20%

Gold Product = 15%

Silver product = 10%

Bronze Product = 5%

According to given condition

Platinum Product sale Commission = Gold Product sale Commission + Bronze Product sale Commission

Platinum Product sale x 20% = Gold Product sale x 15% + Bronze Product sale 5%

Platinum Product sale x 0.2 = $1000 x 0.15 + $15000 x 0.05

Platinum Product sale x 0.2 = $150 + $750

Platinum Product sale x 0.2 = 900

Platinum Product sale = 900 / 0.2 = $4,500

4) $4,500

Explanation:

Step 1: Calculation of total commissions earned from a combined sale of $1,000 in Gold products and $15,000 in Bronze products .

Commissions earned from Gold = Gold sales amount × Commission rate

                                                     = $1,000 × 15%

Commissions earned from Gold = $150

Commissions earned from Bronze = Bronze sales amount × Commission rate

                                                         = $15,000 × 5%

Commissions earned from Bronze = $750

Total commissions earned from Gold and Bronze sales = $150 + $750 = $900

Step 2: Calculation of the amount a salesperson need to sell in Platinum products in order to equal the total commissions earned from a combined sale of $1,000 in Gold products and $15,000 in Bronze products.

Commissions earned from Platinum = Platinum sales amount × Platinum commission rate

To calculation of the amount a salesperson need to sell in Platinum products in order to equal the total commissions earned from a combined sale of $1,000 in Gold products and $15,000 in Bronze products, we set the commissions earned from Platinum equal to the total commissions earned from Gold and Bronze sales as follows:

Platinum sales amount × Commission rate = $900

Since the platinum commission rate is 20% or 0.2, we have:

Platinum sales amount × 0.2 = $900

Platinum sales amount = $900 ÷ 0.2 = $4,500

Therefore, a salesperson need to sell $4,500 in Platinum products in order to equal the total commissions earned from a combined sale of $1,000 in Gold products and $15,000 in Bronze products.

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