# Price and commission

#### chihuaha11

##### New member
My daughter has a math problem that we have been working on for 2 days and we can get the right answer or working.
The question is, a real estate agent earns commission according to the following rules:- 5% on the first \$60,000 and 2.5% on the remainder. What is the minimum price a property could sell for in order for the seller to receive \$400,000 after commission? Can any one help us?

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#### Jameson

The question is, a real estate agent earns commission according to the following rules:- 5% on the first \$60,000 and 2.5% on the remainder. What is the minimum price a property could sell for in order for the seller to receive \$400,000 after commission? Can any one help us?
The basic set up goes like this: $$\displaystyle P-C=400,000$$ where P is the price of the house and C is the commission to the real estate agent. Now the question is how can we express the commission in terms of the price of the house? If the house is greater than \$60,000 then the commission is $$\displaystyle (0.05)(60,000)+(0.025)(P-60,000)$$. So substitute in the above expression for C into the first equation and solve for P. Make sense? Jameson Last edited: • Sudharaka #### chihuaha11 ##### New member Re: need some math homework help hi, thank you for your reply, but my daughter still doesn't understand. This is her working for your equations; P- C = 400, 000 where C = (0.05x60,000) + 0.025(P-60, 000) 400, 000 = P - (0.05x60,000) + 0.025(P-60, 000) 400, 000 = P - 3, 000 + 0.025(P-60, 000) 403, 000 = P + (0.025 x P) - (0.025 x 60, 000) 403, 000 = P + (0.025 x P) - 1, 500 404, 500 = P + (0.025 x P) This is a far as she has come and is unsure how to proceed as P appears twice in the equation. Any help is greatly appreciated. Thank you #### Jameson ##### Administrator Staff member Re: need some math homework help $$\displaystyle 400,000 = P - \left( 0.05 \times 60,000+0.025 \times (P-60,000) \right)$$ $$\displaystyle 400,000 = P - \left( 3000+0.025P-1500 \right)$$ $$\displaystyle 400,000= P - \left(0.025P+1500 \right)$$ $$\displaystyle 400,000 = P-0.025P-1500$$ $$\displaystyle 401,500=0.975P$$ $$\displaystyle P=\frac{401,500}{0.975}=\411,794.87$$ • chihuaha11 #### chihuaha11 ##### New member Re: need some math homework help Thank you very much. This makes so much more sense now. I will apply this solution to a similar problem and test if i can do it myself. Thanks again, your a legend! #### Wilmer ##### In Memoriam Re: need some math homework help If you're trying "to see by doing some yourself", go this way (in reverse!): Code: MSP 500,000.00 -( 60000 * .05) -3,000.00 -(440000 * .025) -14,000.00 ========== NET 486,000.00 This would be: find Minimum Selling Price in order to net$486,000;
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