A real estate agent to sell a large apartment complex according to the following commission schedule: $45,000 plus 25% of the selling price in excess of $900,000. Assuming that the complex will sell at some price between $900,000 and $1,100,000, inclusive, over what range does the agent's commission vary? How does the commission vary as a percent of selling price?
how to solve this?
I don't know how to set this up.
the equation.
Info:
45,000 + 0.25
excess 900,000
inclusive 900,000 to 1,100,000
so for the "price" I put in 900,000 and then 1,100,000?
Also to find the percent
the commission would be 45,000 and 95,000
but, what would be the selling price ?
To solve this problem, we need to calculate the range of the agent's commission and determine how the commission varies as a percentage of the selling price. Here's how you can do it:
1. Calculate the maximum commission:
- The flat fee is $45,000.
- The selling price in excess of $900,000 is $1,100,000 - $900,000 = $200,000.
- The commission on the excess selling price is 25%, which translates to 0.25.
- Multiply the excess selling price by the commission rate: $200,000 * 0.25 = $50,000.
- Add the flat fee and the commission on the excess selling price: $45,000 + $50,000 = $95,000.
- The maximum commission is $95,000.
2. Calculate the minimum commission:
- The flat fee is still $45,000.
- The selling price in this case is the lower bound, which is $900,000.
- Since the selling price is equal to $900,000, the excess selling price is zero ($900,000 - $900,000 = $0).
- Multiply the excess selling price by the commission rate: $0 * 0.25 = $0.
- Add the flat fee and the commission on the excess selling price: $45,000 + $0 = $45,000.
- The minimum commission is $45,000.
3. Calculate the commission range:
- Subtract the minimum commission from the maximum commission: $95,000 - $45,000 = $50,000.
- The commission range is $50,000.
4. Calculate the commission as a percentage of selling price:
- Divide the commission range by the difference between the maximum and minimum selling prices: $50,000 / ($1,100,000 - $900,000) = $50,000 / $200,000 = 0.25.
- Multiply the result by 100 to express it as a percentage: 0.25 * 100 = 25%.
- The commission varies as 25% of the selling price.
Therefore, the agent's commission varies in the range of $45,000 to $95,000, and it represents 25% of the selling price.
commission= 45,000+.25(Price-900,000)
figure commission on price of 900,000, then commission on 1,100,000
then figure percent:
percent=commission/sellingprice x 100%