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QuestionA seller got \$321,480 after a 6% broker's fee. What was the sale price: \$342,000 or \$345,000?

Studdy Solution

STEP 1

Assumptions1. The seller received \$321,480 after a6% deduction for the broker's fee. . The possible sale prices are \$342,000 and \$345,000.
3. The broker's fee is calculated as a percentage of the sale price.

STEP 2

First, we need to express the broker's fee as a percentage of the sale price. This can be done by subtracting the percentage of the broker's fee from100%.
Sale price=Received amount/(1−Broker′s fee percentage)Sale\, price = Received\, amount / (1 - Broker's\, fee\, percentage)

STEP 3

Convert the broker's fee percentage to a decimal value.
6%=0.066\% =0.06

STEP 4

Now, plug in the given values for the received amount and broker's fee percentage to calculate the sale price.
Sale price=$321,480/(1−0.06)Sale\, price = \$321,480 / (1 -0.06)

STEP 5

Calculate the sale price.
Sale price=$321,480/0.94=$342,000Sale\, price = \$321,480 /0.94 = \$342,000The sale price was \$342,000.

STEP 6

To confirm, let's calculate the broker's fee using the sale price and check if it matches the given deduction.
Broker′s fee=Sale pricetimesBroker′s fee percentageBroker's\, fee = Sale\, price \\times Broker's\, fee\, percentage

STEP 7

Plug in the values for the sale price and the broker's fee percentage to calculate the broker's fee.
Broker′s fee=$342,000times0.06Broker's\, fee = \$342,000 \\times0.06

STEP 8

Calculate the broker's fee.
Broker′s fee=$342,000times0.06=$20,520Broker's\, fee = \$342,000 \\times0.06 = \$20,520

STEP 9

Now, subtract the broker's fee from the sale price to check if it matches the received amount.
Received amount=Sale price−Broker′s feeReceived\, amount = Sale\, price - Broker's\, fee

STEP 10

Plug in the values for the sale price and the broker's fee to calculate the received amount.
Received amount=$342,000−$20,520Received\, amount = \$342,000 - \$20,520

STEP 11

Calculate the received amount.
Received amount=$342,000−$20,520=$321,480Received\, amount = \$342,000 - \$20,520 = \$321,480The received amount matches the given value, so the sale price was \$342,000.

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