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Math Help - animals heads legs chickens

  1. #1
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    ratios

    my 11yr old has been given some homework on ratios that i'm finding hard,
    A farm has some chickens & some rabbits.
    Altogether there are:
    35 heads
    94 legs
    How many chickens are there?
    and how many rabbits are there?
    plus show your workings
    Any help would be great
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  2. #2
    MHF Contributor
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    Quote Originally Posted by lacourse
    my 11yr old has been given some homework on ratios that i'm finding hard,
    A farm has some chickens & some rabbits.
    Altogether there are:
    35 heads
    94 legs
    How many chickens are there?
    and how many rabbits are there?
    plus show your workings
    Any help would be great
    So it is about heads and legs.
    Chicken has one head; rabbit has one head.
    Chicken has two legs; rabbit has 4 legs.

    Let c = number of chickens in there; and r = number of rabbits.

    Re heads:
    c*1 +r*1 = 35
    c +r = 35 -------------(1)

    Re legs:
    c*2 +r*4 = 94
    2c +4r = 94
    Reduce that to its "lowest term", divide both sides by 2,
    c +2r = 47 ------------(2)

    One way to continue is by substitution.
    From (1), c = 35-r
    Substitute that into (2),
    35-r +2r = 47
    2r -r = 47 -35
    r = 12
    So, c = 35 -12 = 23

    Therefore, there are 23 chickens and 12 rabbits in there. ------answer.

    ---------
    Check.

    Re heads,
    c +r = 35
    23 +12 =? 35
    35 =? 35
    Yes, so, OK.

    Re legs,
    2c +4r = 94
    2*23 +4*12 =? 94
    46 +48 =? 94
    94 =? 94
    Yes, so, OK.
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by lacourse
    my 11yr old has been given some homework on ratios that i'm finding hard,
    A farm has some chickens & some rabbits.
    Altogether there are:
    35 heads
    94 legs
    How many chickens are there?
    and how many rabbits are there?
    plus show your workings
    Any help would be great
    As there are 35 heads we have 35 creatures altogether.
    Counting two legs of each would account for a total of
    70 legs, leaving 24 legs unaccounted for, which must
    belong to 12 rabbits (to give each rabbit four legs)

    So we have 12 rabbits and 23 chickens.

    RonL
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  4. #4
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    Thanks,
    My daughter will be pleased
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