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April 18th, 2019, 09:01 AM   #1
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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 litres
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April 18th, 2019, 09:44 AM   #2
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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:

$\displaystyle 120x+30y = 3000$
$\displaystyle y = 100-4x$

But i'm not sure where to go from here since there isn't any information on the number of motorists that showed up.
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April 18th, 2019, 10:26 AM   #3
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Quote:
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 given ratio of motorist to motorcyclist = 1:4 $\implies$ the 3000 L of fuel was dispensed in a 600:2400 ratio, motorists to motorcyclists

If each motorcyclist received 30 L, then 2400/30 = 80 motorcyclists were served.
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April 18th, 2019, 11:09 AM   #4
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Quote:
How many motorcyclist were served from 3 000 liters of fuel if each collects 30 liters?
I think the problem I had here was that I did not know that 3 000 litres of fuel was served to both motorists and motorcyclist. Initially, I thought the 3000 litres of fuel was only served to motorcyclist. But in your own judgement of wording or grammar, do you think How many motorcyclist were served from 3 000 liters of fuel if each collects 30 liters? mean that only motorcyclists were served 3 000 litres of fuel as I thought initially or it means both motorists and motorcyclists were served the same litres in the same ratio?

Last edited by Chikis; April 18th, 2019 at 11:16 AM.
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April 18th, 2019, 11:18 AM   #5
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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.
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April 18th, 2019, 11:49 AM   #6
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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?
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April 18th, 2019, 04:04 PM   #7
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Not wrong ... maybe he/she could have worded it better.

Last edited by skeeter; April 18th, 2019 at 04:07 PM.
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April 19th, 2019, 07:16 AM   #8
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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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