A broker receives 40% of the commission. If the seller received $43,500 after a 7% fee, how much did the broker earn?

A broker receives 40% of the commission. If the seller received $43,500 after a 7% fee, how much did the broker earn?

• A. $3,275.
• B. $3,045.
• C. $1,310.
• D. $1,218.

Answer: (C)

To determine how much the broker earned, we first need to calculate the total commission based on the seller’s proceeds after the fee is deducted. The seller receives $43,500 after a 7% commission has been taken from the sale price. Let’s denote the sale price as "P." The fee is 7% of "P," which means the seller receives 93% of "P." We can express this mathematically as: \[ 0.93P = 43,500 \] To find "P," we can rearrange the equation: \[ P = \frac{43,500}{0.93} \] \[ P = 46,774.19 \] (approximately) Next, we calculate the total commission, which is 7% of the sale price "P": \[ \text{Total Commission} = 0.07 \times P \] \[ \text{Total Commission} = 0.07 \times 46,774.19 \] \[ \text{Total Commission} = 3,273.19 \] (approximately) Now, according to the problem, the broker receives 40% of this total commission: \[ \text{Broker's Earnings} =

To determine how much the broker earned, we first need to calculate the total commission based on the seller’s proceeds after the fee is deducted. The seller receives $43,500 after a 7% commission has been taken from the sale price.

Let’s denote the sale price as "P." The fee is 7% of "P," which means the seller receives 93% of "P." We can express this mathematically as:

[ 0.93P = 43,500 ]

To find "P," we can rearrange the equation:

[ P = \frac{43,500}{0.93} ]

[ P = 46,774.19 ] (approximately)

Next, we calculate the total commission, which is 7% of the sale price "P":

[ \text{Total Commission} = 0.07 \times P ]

[ \text{Total Commission} = 0.07 \times 46,774.19 ]

[ \text{Total Commission} = 3,273.19 ] (approximately)

Now, according to the problem, the broker receives 40% of this total commission:

[ \text{Broker's Earnings} =