Can this be solved?

[stefk]

Hi, can this be solved?
X-Y=2.4
also we know the % difference from X and Y = 2

Can you explain the maths to me please

Thanks

 

[Deleted member 4993]

Hi, can this be solved?
X-Y=2.4
also we know the % difference from X and Y = 2

Can you explain the maths to me please

Thanks

Hint:

Express

"... % difference from X and Y = 2"​

as a mathematical equation.​

Now you will have two equations & two unknowns and solve!

Please share your work/thoughts with us.

 

[stefk]

Damn, wasn't really looking for a math's lessons but more so for a quick answer

Ill give it a shot though..



2% = 0.02 = 2.4 / X * 100
x = 12000
feels wrong

 

[HallsofIvy]

"% difference between X and Y" is ambiguous. Is the "difference" X- Y or Y- X? Is the "percent difference" \(\displaystyle \frac{X- Y}{Y}\) or \(\displaystyle \frac{X- Y}{X}\) or \(\displaystyle \frac{Y- X}{Y}\) or \(\displaystyle \frac{X- Y}{X}\)?

If it is \(\displaystyle \frac{X- Y}{Y}= 0.02\) then X- Y= 0.02Y or X= 1.02Y.

We have X= Y+2.4, 1.02Y- Y= 0.02Y= 2.4. Y= 2.4/0.02= 120 and X= 1.02(120)= 122.4,

The "difference" is X- Y= 122.4- 120= 2.4 and the "percent difference" is \(\displaystyle \frac{2.4}{120}= 0.02\) or 2%.

(Thanks to Cubist for a correction.)

 

[Cubist]

Damn, wasn't really looking for a math's lessons but more so for a quick answer

If we help you to solve the problem yourself, then next time you'll be able to answer it without having to ask! That's what we try to accomplish on this forum.

@HallsofIvy is correct about the ambiguity. Therefore some context would be very helpful. Are you helping out a child with their schoolwork? If so then it might help if you can find a similar worded problem, in their textbook, that is given as an example (and post it here).

Here is another possibility:- it could mean, "the percentage difference between (not "from") X and Y is 2%" (see percentage-difference). This would imply...

2 = 100 * difference / average = 100 * (X-Y) / ( (X+Y)/2 ) = 200*(X - Y)/(X + Y)

Please explain where you found this problem and it might help to shed some extra light on it.

EDIT: Also, please double check the exact wording of the problem

 

[stefk]

Thanks for your replies.

It started of being a personal problem I was trying to figure out (and just wanted an answer) but now I'm intrigued by how to solve it.
I believe I expressed it wrong and meant the percentage difference between (not "from") as Cubist mentioned above

The question is can we figure out the original two numbers if we know the difference between them and the % of that difference

So if the % difference is ambiguous then this cant be done?

in content: if we know someone lost $2 and that loss was a 2.4% loss from the starting investment to the exit, can we figure out the starting and ending money involved?

thanks

edit: i guess it cant - feeling a bit silly now

 

[Cubist]

if we know someone lost $2 and that loss was a 2.4% loss from the starting investment to the exit, can we figure out the starting and ending money involved?

Thanks for providing this description which makes things more clear. When writing this you (probably) used the correct phrasing without realizing it, "percentage loss from starting investment to exit". In this circumstance the percentage will be relative to the original investment.

BUT to add to the confusion you seem to have swapped the numbers around. I'll assume that you meant to say, "if we know someone lost $2.4 and that loss was a 2% loss from the starting investment to the exit"

Now we can calculate the amounts with some extra certainty...

X=Amount originally invested
Y=Returned amount at exit

[math]X-Y=2.4 \,[/math] (amount lost)

[math]\dfrac{100(X-Y)}{X}=2 \,[/math] (percentage loss from starting investment to exit)

Reading between the lines it seems that you're not a math student, so I'll work it out for you. Substitute Y=X-2.4 into the second equation to obtain...

[math] \dfrac{100(X-(X-2.4))}{X}=2 [/math]
[math] \dfrac{100(2.4)}{X}=2[/math]
[math]100\times2.4=2X[/math]
[math]240=2X[/math]
[math]X=120[/math]
Putting X value back into the first equation gives...

[math]120-Y=2.4[/math]
[math]Y=120-2.4[/math]
[math]Y=117.6[/math]
NOTE: percentage calculations depend on the wording and context to avoid ambiguity
NOTE2: If the numbers are actually the other way around, then hopefully you can now repeat the procedure above yourself using the different numbers.

 

[stefk]

Many thanks for the explanation and the working out
Interesting maths