The story of the four brothers

Algebra Level 2

Four brothers have a total of of 45 coins.The coins are then distributed to the four of them in a certain ratio.If the money of the first is increased by 2, and the money of the second is decreased by 2,and the money of the third is doubled, and the money of the fourth is halved,then all of them have the same amount of money.How many coins does the second brother have?


The answer is 12.

Anik Mandal by Anik Mandal , 21, India

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1 solution

Ritwic Majumder
Jan 13, 2015

Let the four brothers have a,b,c and d coins respectively. Therefore, a + b + c + d = 45 a+b+c+d=45 and a + 2 = b − 2 = 2 c = d 2 a+2=b-2=2c=\frac{d}{2} . Then, a = 2 c − 2 , b = 2 c + 2 , d = 4 c a=2c-2 , b=2c+2 , d=4c . Substituting the value of a,b and d in the first equation : 2 c − 2 + 2 c + 2 + c + 4 c = 45 2c-2+2c+2+c+4c=45 or c = 5 c=5 . Therefore , b = 2 ( 5 ) + 2 = 12 b=2(5)+2=12

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