MHB How Do You Calculate Loss Percentage in a Quadratic Equation Problem?

AI Thread Summary
To calculate the loss percentage in the horse selling scenario, the cost price (C) is key to determining the loss. The loss is defined as the difference between the cost price and the selling price, which is $C - 72. The loss percentage can be expressed in different ways, leading to multiple interpretations of the problem. The most likely interpretation involves using the selling price, leading to the equation where the loss percentage equals one-eighth of the cost price. Ultimately, the discussion emphasizes the importance of correctly interpreting the loss percentage to solve the problem effectively.
NotaMathPerson
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A person, selling a horse for $72, finds that his loss per cent is one-eight of the number of dollars that he paid for the horse; what was the cost price?

Can anybody explain the part " loss per cent" and how do I express that algebraically. Thanks!
 
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NotaMathPerson said:
A person, selling a horse for $72, finds that his loss per cent is one-eight of the number of dollars that he paid for the horse; what was the cost price?

Can anybody explain the part " loss per cent" and how do I express that algebraically. Thanks!

Hey NotaMathPerson! ;)

That is quite ambiguous.

Suppose the cost price is $C$, then his loss is $C - 72$.

It could mean:
1. His loss per cent of the cost price (which would be my expectation). That would mean that we have $\frac{C-72}{100C} = \frac C 8$.
2. His loss per cent of the selling price. That would mean that we have $\frac{C-72}{7200} = \frac C 8$.
3. If there is a typo, his loss percentage of the cost price, meaning $\frac{C-72}{C} = \frac C 8$.
4. If there is a typo, his loss percentage of the selling price, meaning $\frac{C-72}{72} = \frac C 8$.

Options 1 and 3 do not have a solution, so for now I'm inclined to assume we're talking about option 2, but seeing the result I wouldn't be surprised if option 4 was intended.
Anyway, how about solving it for option 2? (Wondering)

EDIT: I have just noticed that your title mentions solving a quadratic equation.
That suggests that option 1 is intended after all...
 
Looks to me like your teacher is getting ready to show the class
that a percentage is really a fraction; like 20% = 20/100 = 1/5.

With your problem: 1/8 = .125, or 12.5%.
82.28 - .125*82.22 = 82.28 - 10.28 = 72.
 
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