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July 15th, 2017, 10:58 AM  #1 
Newbie Joined: Dec 2010 Posts: 13 Thanks: 0  A tricky question
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 addon X) The pet adds 6% of all points. (count as addon 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 by Kavesat; July 15th, 2017 at 11:16 AM. 
July 15th, 2017, 12:03 PM  #2  
Senior Member Joined: Sep 2015 From: CA Posts: 1,265 Thanks: 650  Quote:
$FSTR=3027 + X + Y = 3027 + 0.25 FSTR + 0.06 FSTR$ $FSTR = 3027 + 0.31 FSTR$ $0.69 FSTR = 3027$ $FSTR = \dfrac{3027}{0.69}$ $X = \dfrac{0.25}{0.69}\cdot 3027 \approx 1096.7$ $Y = \dfrac{0.06}{0.69}\cdot 3027 \approx 263.2$  
July 15th, 2017, 01:17 PM  #3  
Newbie Joined: Dec 2010 Posts: 13 Thanks: 0  Quote:
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 by Kavesat; July 15th, 2017 at 01:21 PM.  
July 15th, 2017, 02:58 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 17,533 Thanks: 1322 
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).

July 15th, 2017, 04:59 PM  #5  
Newbie Joined: Dec 2010 Posts: 13 Thanks: 0  Quote:
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 skipjack; July 17th, 2017 at 03:19 AM.  
July 15th, 2017, 06:17 PM  #6  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 9,822 Thanks: 651  Quote:
price before discounts: 1000 1st discount: 20% 2nd discount: 10% of (1000  20%) net: ? Your problem can be solved similarly. Last edited by skipjack; July 17th, 2017 at 03:20 AM.  
July 17th, 2017, 02:34 AM  #7  
Newbie Joined: Dec 2010 Posts: 13 Thanks: 0  Quote:
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. Hmm, it looks like it can be calculated directly without worrying about the other variable. Last edited by skipjack; July 17th, 2017 at 03:21 AM.  

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