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Math Help - Basic problem

  1. #1
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    Basic problem

    Hey there!
    I'm having alot of trouble with the following:

    2 types of sacks
    Large sacks weigh 30kg
    Small sacks weigh 24kg
    There are 3 times as much small sacks than there are large ones
    The total weight of sacks is 714kg
    How many large/small sacks are there?


    All ive been able to do is
    30x+24y=714
    not sure how to continue
    Please help
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  2. #2
    MHF Contributor
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    Quote Originally Posted by matchbox View Post
    Hey there!
    I'm having alot of trouble with the following:

    2 types of sacks
    Large sacks weigh 30kg
    Small sacks weigh 24kg
    There are 3 times as much small sacks than there are large ones
    The total weight of sacks is 714kg
    How many large/small sacks are there?


    All ive been able to do is
    30x+24y=714
    not sure how to continue
    Please help
    You forgot to formulate the blue line.

    That then gives a pair of simultaneous equations for the two variables.
    Or you can directly substitute.
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  3. #3
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    Quote Originally Posted by Archie Meade View Post
    You forgot to formulate the blue line.

    That then gives a pair of simultaneous equations for the two variables.
    Or you can directly substitute.
    Aye, just really not sure how to do that
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  4. #4
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    Quote Originally Posted by matchbox View Post
    Aye, just really not sure how to do that
    Ok,

    you have labelled the large sacks "x"
    and the small sacks "y"

    hence y=3x is how we write "there are 3 times as many small sacks as large ones".

    Whatever x is, y is 3 times that.

    Now you have a choice....

    (i) replace y with 3x in 30x+24y=714 to get 30x+24(3x)=714

    and solve for x

    (ii) solve the system of equations

    3x=y
    30x+24y=714

    30x-10y=0
    30x+24y=714

    subtract the first line from the 2nd to get 34y=714

    solve for y
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  5. #5
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    Now i understand. Thanks again
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