Percentage issue without any known values

S

seniij

New member
Joined
Jul 30, 2022
Messages
5
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.
 
seniij said:
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.
Click to expand...
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.

Please follow the rules of posting in this forum, as enunciated at:


Please share your work/thoughts about this problem
 
seniij said:
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?
Click to expand...
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?

My ideas are to pick a symbol for the original amount and then use algebra to write expressions for both values. We could finish by simplifying their ratio.

Have you worked with percents and percentages?

Also, I'm curious about this statement: A product's value increases by x percent and then decreases by x percent. Would the meaning be the same, if we were to delete the word "product's"? The answer doesn't seem to depend on how the original value arises.

:)

[imath]\;[/imath]
 
Subhotosh Khan said:
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.

Please follow the rules of posting in this forum, as enunciated at:


Please share your work/thoughts about this proble
Click to expand...
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.
 
seniij said:
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.
Click to expand...
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]
 
Last edited:
seniij said:
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.
Click to expand...
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?
 
seniij said:
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]
Click to expand...
What you have is NOT correct.

\(\displaystyle V+\frac{Vx}{100}*(1-\frac{x}{100}) = V + \frac{Vx}{100} - \frac{Vx^2}{10,000}\)
 
BigBeachBanana said:
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]
Click to expand...
Solved!

Thank you, after calculating Final/Initial it came to: [math]1-\frac{x^2}{10000}[/math] This was marked almost correct by the question with a hint to change it to percentage: [math]100-\frac{x^2}{100}[/math]
Thank you so much for the help :)

Edit: And also thank you for the hint of saving some algebra. I'm trying to build the calculation routine and these kind of hints really help with that.
 
Subhotosh Khan said:
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?
Click to expand...
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.
 
Steven G said:
What you have is NOT correct.

\(\displaystyle V+\frac{Vx}{100}*(1-\frac{x}{100}) = V + \frac{Vx}{100} - \frac{Vx^2}{10,000}\)
Click to expand...
Ahh, that's true. Missing the brackets from the first one, was meant write:

[math](V+\frac{Vx}{100})*(1-\frac{x}{100}) = V + \frac{Vx}{100}- \frac{Vx}{100} - \frac{Vx^2}{10,000}[/math]
 
seniij said:
change it to [percent]: \(\displaystyle 100-\frac{x^2}{100}\)
Click to expand...
Hi. If they want that form (obtained from multiplying by 100), then you need to include the percent sign.

\(\displaystyle \bigg( 100 \;–\; \frac{x^2}{100} \bigg)\%\)

:)

[imath]\;[/imath]
 
You must log in or register to reply here.
Top