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April 18th, 2019, 09:01 AM  #1 
Senior Member Joined: Jan 2012 Posts: 745 Thanks: 7  How many motorcyclists were served?
During fuel scarcity, a fuel station served fuel to motorist and motorcyclist in the ratio 1:4. How many motorcyclist were served from 3 000 liters of fuel if each collects 30 liters? The only meaning I can make from the problem is that if 3 000 litres of fuel is served to motorcyclist such that each motorcyclist collect 30 litres then the number of motorcyclist served is (3000)/30 = 100 Again, another understanding I have from the ratio 1:4 given, for each one litre a motorcyclist, a motorist get 4 litres Apart this two meanings, I don't seem to get any relationship between the ratio 1:4 and 3 000 litres of fuel and when each motorcyclist collect 30 litresThank you 
April 18th, 2019, 09:44 AM  #2 
Member Joined: Oct 2018 From: USA Posts: 88 Thanks: 61 Math Focus: Algebraic Geometry 
So if the ratio for motorists:motorcyclists is 4:1, if motorcyclists get 30 then motorists should get 120. Where $x$ is the number of motorists and $y$ is the number of motorcyclists: $\displaystyle 120x+30y = 3000$ $\displaystyle y = 1004x$ But i'm not sure where to go from here since there isn't any information on the number of motorists that showed up. 
April 18th, 2019, 10:26 AM  #3  
Math Team Joined: Jul 2011 From: Texas Posts: 3,002 Thanks: 1587  Quote:
If each motorcyclist received 30 L, then 2400/30 = 80 motorcyclists were served.  
April 18th, 2019, 11:09 AM  #4  
Senior Member Joined: Jan 2012 Posts: 745 Thanks: 7  Quote:
Last edited by Chikis; April 18th, 2019 at 11:16 AM.  
April 18th, 2019, 11:18 AM  #5 
Math Team Joined: Jul 2011 From: Texas Posts: 3,002 Thanks: 1587 
I interpreted the 3000L to be the total fuel dispensed to both motorists & motorcyclists, otherwise, the problem is trivial division ... why bother with the ratio information?
Last edited by skeeter; April 18th, 2019 at 11:36 AM. 
April 18th, 2019, 11:49 AM  #6 
Senior Member Joined: Jan 2012 Posts: 745 Thanks: 7 
Thanks for the interpretation. Your interpretation is very correct! But let's face the fact. Do you think the author is wrong in the wording of the problem?

April 18th, 2019, 04:04 PM  #7 
Math Team Joined: Jul 2011 From: Texas Posts: 3,002 Thanks: 1587 
Not wrong ... maybe he/she could have worded it better.
Last edited by skeeter; April 18th, 2019 at 04:07 PM. 
April 19th, 2019, 07:16 AM  #8 
Global Moderator Joined: Dec 2006 Posts: 20,919 Thanks: 2203 
The problem states that there is fuel scarcity and that the fuel is served (rather than sold) to motorist and motorcyclist in the ratio 1:4. This wording suggests that the fuel station is implementing a rationing policy, namely that each motorist will be served 1/4 as much fuel as each motorcyclist. As each motorcyclist is served 30 l of fuel, that would mean that each motorist is served 7.5 l of fuel. The above seems to be a reasonable interpretation of the problem, but it means that more information would be needed to solve it, as the only equation available would be $30x + 7.5y = 3000$, where there are $x$ motorcyclists served and $y$ motorists served (and each variable is a positive integer). This allows $x$ to be any integer from 1 to 99, and $y$ correspondingly to be $400  4x$. 

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