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

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} =