Assume that the product's value was $V to start with. What is "x" percent of "V"?Any ideas how to solve this?
The problem in question:
A products's value increases x percent and then decreases x percent. How many percent is the final value from the original value? Give an exact value that includes the variable x.
Hi seniij. I have some ideas. First, I think the question is, "The final value is what percent of the original value". Or, is it supposed to be about percent change?Any ideas how to solve this?
A products's value increases [by] x percent and then decreases [by] x percent. How many percent is the final value from the original value?
So here is where I am at the moment:Assume that the product's value was $V to start with. What is "x" percent of "V"?
Please show us what you have tried and exactly where you are stuck.
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Please share your work/thoughts about this proble
Your work is correct up until the very last where you're taking the ratio. Note that the question is asking for the "final value compared to original".So here is where I am at the moment:
Let V be the original value and x the percentage change.
Increased value would then be [math]V * (1+\frac{x}{100})[/math] or [math]V+\frac{Vx}{100}[/math].
The final value can then be calculated by: [math]V+\frac{Vx}{100}*(1-\frac{x}{100}) = V-\frac{Vx}{100}+\frac{Vx}{100}-\frac{Vx^2}{10000}[/math] or [math]V-\frac{Vx^2}{10000}[/math]
The percentage of the final from the original value would then be: [math]\frac{V}{V-\frac{Vx^2}{10000}}[/math] or [math]\frac{V*(1)}{V*(1-\frac{x^2}{10000})}[/math] this comes to: [math]\frac{1}{1-\frac{x^2}{10000}}[/math].
I though that would be the final answer, but the exercise says it's incorrect.
Suppose the original Value (V) of the product = 100Any ideas how to solve this?
The problem in question:
A products's value increases x percent and then decreases x percent. How many percent is the final value from the original value? Give an exact value that includes the variable x.
What you have is NOT correct.The final value can then be calculated by: [math]V+\frac{Vx}{100}*(1-\frac{x}{100}) = V-\frac{Vx}{100}+\frac{Vx}{100}-\frac{Vx^2}{10000}[/math]
Solved!Your work is correct up until the very last where you're taking the ratio. Note that the question is asking for the "final value compared to original".
So you would want to Final/Initial. You did the other way around.
Side note: You didn't have to expand out all the terms and notice the difference of squares [imath](a+b)(a-b)=a^2-b^2[/imath]. It would've saved you some algebra.
[math]Final=V\left(1+\frac{x}{100}\right)\left(1-\frac{x}{100}\right)\\ Final=V\left(1-\frac{x^2}{10000}\right) [/math]
I was playing with this as well and used it to check the results of the my calculations, but couldn't get any further to defining the value by using x this way.Suppose the original Value (V) of the product = 100
Increases 10% (x = 10) → Now the value (price) = 110
Decreases 10% (x = 10) → Now the value (price) = 110 - 11 = 99
How many percent is the final value from the original value?= 100 - 99 = 1 ........ so according to my interpretation of FIND, the final value is 1% away from the original value
What value do you get from your derived formula?
Ahh, that's true. Missing the brackets from the first one, was meant write:What you have is NOT correct.
\(\displaystyle V+\frac{Vx}{100}*(1-\frac{x}{100}) = V + \frac{Vx}{100} - \frac{Vx^2}{10,000}\)
Hi. If they want that form (obtained from multiplying by 100), then you need to include the percent sign.change it to [percent]: \(\displaystyle 100-\frac{x^2}{100}\)
MAY not be necessary - because "percent" is included in the question already.then you need to include the percent sign
How many percent is the final value from the original value?