SOLUTION: In a jar of red, green, and blue marbles, all but 6 are red marbles, all but 8 are green, and all but 4 are blue. What percent of the marbles aren’t blue?

Algebra ->  Average -> SOLUTION: In a jar of red, green, and blue marbles, all but 6 are red marbles, all but 8 are green, and all but 4 are blue. What percent of the marbles aren’t blue?      Log On


   

Question 1140438: In a jar of red, green, and blue marbles, all but 6 are red marbles, all but 8 are green, and
all but 4 are blue. What percent of the marbles aren’t blue?
Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
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From the condition, we can determine how many marbles of each color were there in the jar.


Indeed, we have these equations, where R is the number of red marbles, G is the number of green marbles and B is the number of blue marbles


    G + B = 6           (1)             ("all but 6 are red marbles")

    R + B = 8           (2)             ("all but 8 are green marbles")

    R + G = 4           (3)             ("all but 4 are blue marbles")


    ------------------------  Add equations (1), (2) and (3)


  2*(R + G + B) = 6 + 8 + 4 = 18   ===========>


     R + G + B = 9.     (4)


Now, subtracting from equation (4) equations (1), (2) and (3), one after one separately, we get


    R = 3;  G = 1;  B = 5.


Now the answer to the problem's question is  


    The ratio is  %283%2B1%29%2F%283%2B1%2B5%29 = 4%2F9;


    The percentage is  %284%2F9%29%2A100 = 44.44%.      ANSWER

Solved.