A tricky question

Dec 2010
19
0
When I first see this, I just doubt there's a solution.
But actually it has a solution. Anyone wanna try this? :)

A man has 3027 STR points. He takes a potion and has a pet.
The potion adds 25% of all points. (count as add-on X)
The pet adds 6% of all points. (count as add-on Y)
The calculation of the potion includes the Y.
The calculation of the pet includes the X.
What value is X and Y?
You can round it to the nearest tenth.
 
Last edited:

romsek

Math Team
Sep 2015
2,958
1,673
USA
When I first see this, I just doubt there's a solution.
But actually it has a solution. Anyone wanna try this? :)

A man has 3027 STR points. He takes a potion and has a pet.
The potion adds 25% of all points. (count as add-on X)
The pet adds 6% of all points. (count as add-on Y)
The calculation of the potion includes the Y.
The calculation of the pet includes the X.
What value is X and Y?
You can round it to the nearest tenth.
it's tough to understand exactly what you mean here but it sounds like you have

$FSTR=3027 + X + Y = 3027 + 0.25 FSTR + 0.06 FSTR$

$FSTR = 3027 + 0.31 FSTR$

$0.69 FSTR = 3027$

$FSTR = \dfrac{3027}{0.69}$

$X = \dfrac{0.25}{0.69}\cdot 3027 \approx 1096.7$

$Y = \dfrac{0.06}{0.69}\cdot 3027 \approx 263.2$
 
Dec 2010
19
0
it's tough to understand exactly what you mean here but it sounds like you have

$FSTR=3027 + X + Y = 3027 + 0.25 FSTR + 0.06 FSTR$

$FSTR = 3027 + 0.31 FSTR$

$0.69 FSTR = 3027$

$FSTR = \dfrac{3027}{0.69}$

$X = \dfrac{0.25}{0.69}\cdot 3027 \approx 1096.7$

$Y = \dfrac{0.06}{0.69}\cdot 3027 \approx 263.2$
Thanks for reply. :)
Well, it seems wrong because if you try to check calculation.
(1096+3027)*0.06=247
It doesn't correspond with the pet Y 263
As the statement says,
The calculation of the potion includes the Y.
The calculation of the pet includes the X.
There is actually a value that can correspond with each other.
 
Last edited:

skipjack

Forum Staff
Dec 2006
21,473
2,466
If the problem means that X = 25% of (3027 + Y) and Y = 6% of (3027 + X), it's easy to solve those to get X = 814.4 and Y = 230.5 (both rounded to the nearest tenth of a point).
 
Dec 2010
19
0
If the problem means that X = 25% of (3027 + Y) and Y = 6% of (3027 + X), it's easy to solve those to get X = 814.4 and Y = 230.5 (both rounded to the nearest tenth of a point).
Yes, you got it. :)
It is still somewhat tricky because in practice if you want to try to measure something X (like the potion) that is related to something Y (pet), but the Y can't be determined itself value because it requires to know the X's value FIRST, then you can't calculate the X, either. That's why I first time encountered this and confused for a while without thinking deeply of using equations.

My previous calculation:

3027 +x
x is x

(3027 +x)*0.06= y

[3027+(3027 +x)*0.06]*0.25=x
[3027+181.62+0.06x]*0.25=x
[3208.62+0.06x]*0.25=x
802.155+0.015x=x
x=814.370558376~814.4
y=230.482233503~230.5
 
Last edited by a moderator:

Denis

Math Team
Oct 2011
14,592
1,026
Ottawa Ontario, Canada
It is still somewhat tricky because in practice if you want to try to measure something X (like the potion) that is related to something Y (pet), but the Y can't be determined itself value because it requires to know the X's value FIRST, then you can't calculate the X, either.
Try something similar but simpler; as example:
price before discounts: 1000
1st discount: 20%
2nd discount: 10% of (1000 - 20%)
net: ?

Your problem can be solved similarly.
 
Last edited by a moderator:
Dec 2010
19
0
it's tough to understand exactly what you mean here but it sounds like you have

$FSTR=3027 + X + Y = 3027 + 0.25 FSTR + 0.06 FSTR$

$FSTR = 3027 + 0.31 FSTR$

$0.69 FSTR = 3027$

$FSTR = \dfrac{3027}{0.69}$

$X = \dfrac{0.25}{0.69}\cdot 3027 \approx 1096.7$

$Y = \dfrac{0.06}{0.69}\cdot 3027 \approx 263.2$
Sorry, my bad. I reread all replies. My statement is not clear. I shouldn't use "all points" to misguide you.
In the case of "all points" to calculate each single includes x and y, you are right. Your calculation is brilliant. :)
And I am still a bit surprised that it still can be "calculated" in that case and if there is a case like that in reality.

Try something similar but simpler; as example:
price before discounts: 1000
1st discount: 20%
2nd discount: 10% of (1000 - 20%)
net: ?

Your problem can be solved similarly.
Hmm, it looks like it can be calculated directly without worrying about the other variable.
 
Last edited by a moderator:

Country Boy

Math Team
Jan 2015
3,261
899
Alabama
It is still somewhat tricky because in practice if you want to try to measure something X (like the potion) that is related to something Y (pet), but the Y can't be determined itself value because it requires to know the X's value FIRST, then you can't calculate the X, either. That's why I first time encountered this and confused for a while without thinking deeply of using equations.
That is exactly the kind of problem algebra is intended to solve.
 
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