Wine theft

Algebra Level 4

There was a thief who went to a wine shop to steal wine. He went in at 10pm, stole 10 L of wine and added 10 L of water to top up the barrel. He came back at 1am, stole 10 L of the mixture from the same barrel and added 10 L of water to top it up. In the morning, the ratio of wine to water in the barrel was 144:25. Find the initial amount of wine in the barrel.

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The answer is 130.

Anik Mandal by Anik Mandal , 21, India

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1 solution

Guiseppi Butel
Apr 30, 2014

Solution

1 Helpful 0 Interesting 0 Brilliant 0 Confused

the answer is 130
initial wine water ratio is x:0
after 1st theft we have x-10:10
after 2nd theft we have x-10-((x-10)/x)*10 : 10-100/x+10
solving we would get...(x^2-20x+100)/(20x-100)
but this ratio is equal to 144:25
so equating and solving we would get....25x^2-3380x+16900=0
x=130,5.2
obviously 130 would be the answer


Vignesh Jeganathan - 7 years, 1 month ago

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rearranging correctly the equation becomes 25x^2-3380x+16900

Chirag Jalan - 7 years, 1 month ago

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ya...I made a calculation error...thank u for correcting me....!

Vignesh Jeganathan - 7 years, 1 month ago

I did exactly as written above, but until the last equation, I was too late because it is difficult to factorized. so I just estimated that 130 of its results, and it is true. I hope no one has found a more practical solution than my solution, but it did not.

Rifqi Mukhammad - 6 years, 2 months ago

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