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Math Help - Basic problem...??

  1. #1
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    Basic problem...??

    Hey guys, this is a very basic problem. i worked it out and im not sure if i have the correct answer. its highschool math so it'll be real quick.

    30 learners in a class consisting of boys and girls play hockey and swimming. The ratio for boys of hockey to swimming is 2:3. 6 girls play hockey and 4 swim. If the ration of girls to guys is 2:1, what is the ratio of hockey players to swimmers?

    i got 8 swimmer boys, 12 hockey boys and the final ratio is 3:2. The ratio to for the boys of hockey to swimming isnt correct which is what is bugging me or is it a misunderstanding of the ratio.

    THANKS!
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by outspired View Post
    Hey guys, this is a very basic problem. i worked it out and im not sure if i have the correct answer. its highschool math so it'll be real quick.

    30 learners in a class consisting of boys and girls play hockey and swimming. The ratio for boys of hockey to swimming is 2:3. 6 girls play hockey and 4 swim. If the ration of girls to guys is 2:1, what is the ratio of hockey players to swimmers?

    i got 8 swimmer boys, 12 hockey boys and the final ratio is 3:2. The ratio to for the boys of hockey to swimming isnt correct which is what is bugging me or is it a misunderstanding of the ratio.

    THANKS!
    First note that there are 20 girls and ten boys. This is obtained by adding the terms of the ratio 2:1, that is, 2+1=3, and then dividing the total number of students by this number and then multiplying each term by that value (10).

    Now, with the same thinking, we see that 4 boys play hockey, 6 boys swim, and it was given that 6 girls play hockey and 4 swim (which doesn't really make sense because we were told first that the entire class participated in one of the sports, but anyway...).

    So there are 10 hockey players and 10 swimmers.

    Therefore, the ratio of hockey players to swimmers is 10:10, or, more simply, 1:1.
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  3. #3
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    Oct 2009
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    Von, thanks man. Im still abit confused. Here is my logic.

    30 = a+b+c+d ; All the learners are made up of hockey girls/boys and swimmer girl/boys
    ; a = hockey boys, b = swimmer boys, c = hockey girls, d = swimmer girls.

    Therefore:

    30 = a+b +6 + 4
    20 = a+b ; this means that there are 20 boys that play hockey and swim.

    we're told that:

    2a = 3b
    a = (3/2)b

    Therefore:

    20 = (3/2)b + b
    40 = 3b +2b

    b = 8 ;8 swimmer boys

    Therefore:

    a = 12 ;12 hockey boys

    This means that the total ratio of hockey to swimmers is:

    12+6 : 4 + 8
    18:12
    3:2

    Are my equations wrong or is there a misunderstanding of the process?

    Thanks again.
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