A parcel of land described as "the NW 1/4 and the SW 1/4 of Section 6, T4N, R8W of the Third Principal Meridian" was sold for $875 per acre. The listing brokerage will receive a 5% commission on the total sales price. How much will the broker receive?

The broker will receive a total brokerage of $14,000 on such land sold in the ratio of 1/4 of both the NW and SW of the "Third Principle Meridian". The total brokerage to be received will be calculated as 5% of sales.

The amount of commission received by the broker is 5% of total land parcel sold which is to be calculated by using the formula of the "Third Principal Meridian".

The calculation of the amount of brokerage can be determined after calculation of total parcel of land sold which can be shown as below,

[tex]\rm Land\ Sold\ in\ NW= 640\ x\ \dfrac {1}{4}[/tex]

[tex]\rm Land\ Sold\ in\ NW= \dfrac {640}{4}\\\\\\\rm Land\ Sold\ in\ NW= 160\ parcels[/tex]

So in all 160 acres of land was sold in NW. So the calculation of sales will be done as below,

[tex]\rm Sales= Total\ land\ sold\ x\ Rate\ per\ acre\ \\\\\\\rm Sales= 160\ x\ 875\\\\\\\rm Sales = 140000\ USD[/tex]

The land sold in SW can be calculated using similar calculations. As we know that the ratio is equal in case of SW, it can be said that 160 acres was sold in SW as well.

So, sales in SW will be shown as below,

[tex]\rm Sales= Total\ land\ sold\ x\ Rate\ per\ acre\ \\\\\\\rm Sales= 160\ x\ 875\\\\\\\rm Sales = 140000\ USD[/tex]

Now we can calculate the total brokerage received by putting the values in the equation as under,

[tex]\rm Commission= Brokerage\ rate\ x\ Sales\ in\ SW\ and\ NW\\\\\\\rm Commission= 0.05\ x\ 280000\\\\\\\rm Commission = 14000\ USD[/tex]

The broker receives $14,000 as his commission on total sales of 320 acres of land at the rate of $875 per acre.

Hence, the broker receives $14,000 on the total sales of 320 acres.

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