After deducting a 7% brokerage fee, the seller received $43,500. How much did the broker receive if they earned 40% of the commission?

To determine how much the broker received, we first need to calculate the total amount the seller received before the brokerage fee was deducted. The seller received $43,500 after a 7% brokerage fee was applied. This means that the amount the seller received represents 93% of the total sale price because 100% - 7% = 93%.

We can set up the equation to find the total sale price (SP):

0.93 * SP = $43,500

To find SP, divide $43,500 by 0.93:

SP = $43,500 / 0.93

SP = $46,774.73 (approximately)

Now, the total commission earned from this sale is 7% of the total sale price:

Total Commission = 0.07 * SP

Total Commission = 0.07 * $46,774.73

Total Commission = $3,274.23 (approximately)

Since the broker earned 40% of this commission, we can calculate their earnings:

Broker's Earnings = 0.40 * Total Commission

Broker's Earnings = 0.40 * $3,274.23

Broker's Earnings = $1,309.69 (approximately)