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Math Help - word problem equations

  1. #1
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    word problem equations

    I hope you guys can help me... because it's easy but for some reason I can't figure it out? -.-

    1) Two hundred people attend a concert. The total receipts are $4500. If one student ticket costs $5, and one adult ticket costs $30, find the number of students who attend the concert?

    2) A farmer raises some pigs and chickens. Among the pigs and chickens there are 24 heads and 64 feet. How many pigs and chickens are there?

    Substitution only please.

    Come to think of it... maybe you guys can just do one and I can use your steps from the first one to do second
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  2. #2
    Junior Member mathmonster's Avatar
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    from question 1, u can see that if x is number of student and y is number of adults then 200 = x + y,
    and so $4500 = $5x + $30y then use the substitution x = 200 - y
    and go from there
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  3. #3
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    Let x=the Number of tickets sold

    5x+30x=4500
    \Rightarrow 35x=4500
    \Rightarrow x=128.57 Round up if you like
    (128.57)(5)=642.85

    Roughly 642 students attended the concert assuming my equation is correct.
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  4. #4
    Junior Member mathmonster's Avatar
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    OZzman u havent taken into acount the adults also attending!
    and it says in total only 200 ppl attended
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  5. #5
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    Oh yea you're right.
    Last edited by OzzMan; February 8th 2008 at 04:47 PM.
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  6. #6
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    4500=5(200-y)+30y
    4500=1000-5y+30y
    4500=1000+25y
    3500=25y
    y=140

    200-140=60
    60 Students attended
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  7. #7
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    Quote Originally Posted by mathmonster View Post
    from question 1, u can see that if x is number of student and y is number of adults then 200 = x + y,
    and so $4500 = $5x + $30y then use the substitution x = 200 - y
    and go from there
    Where did you get 200 from.

    [EDIT] Nvm, Ozzman answered
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  8. #8
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    Alright, so for question #2, there are 8 pigs and 16 chickens.

    Now, can you guys help me with the harder questions? XD

    Solve using substitution

    1)
    x-5y=8
    4x+26=10

    2)
    3x+2y=16
    3y-x=13

    --

    Solve using elimination

    1)
    2u=3v
    u+2v=7

    2)
    -4x+3y=17
    3x-2y=10

    --

    1) Given two numbers whose difference is 20 such that twice on number equals three times the other. Find the numbers.

    Thanks!
    Last edited by Rocher; February 8th 2008 at 06:54 PM.
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  9. #9
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    Substitution #2

    3x+2y=16

    3y-x=13\quad\Rightarrow -x=(13-3y)\quad\Rightarrow x=-13+3y

    3(-13+3y)+2y=16\quad\Rightarrow -39+9y+2y=16\quad\Rightarrow 11y=55\quad\Rightarrow y=5

    3(5)-x=13\quad\Rightarrow 15-x=13\quad\Rightarrow -x=-2\quad\Rightarrow x=2

    Elimination #1

    2u=3v\quad\Rightarrow 2u-3v=0

    u+2v=7\quad\Rightarrow (u+2v=7)-2\quad\Rightarrow -2u-4v=-14

    Now add the equations 2u-3v=0 and the -2u-4v=14 the u's will cross out leaving v as the only variable

    -7v=-14\quad\Rightarrow v=2

    Now plug v back into the original equation to solve for the other variable u+2(2)=7\quad\Rightarrow u+4=7\quad\Rightarrow u=3
    Last edited by OzzMan; February 9th 2008 at 01:24 AM.
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  10. #10
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    Can you help me do the other ones too? Because I have looked at them and they are nowhere near similar...

    [EDIT] Wait I got the substitution one #2. Now just need elimination and that other question...
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  11. #11
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    Quote Originally Posted by Rocher View Post
    ...

    1) Given two numbers whose difference is 20 such that twice on number equals three times the other. Find the numbers.
    The first number is x
    the second number is y.

    Then you know: x - y = 20 (from this equation you know that x > y)
    and 2x = 3y

    Use substitution: y = x - 20

    2x = 3(x-20) Expand the bracket and collect like terms, x at the LHS.

    -x = -60 that means: x = 60 and therefore y = 40.
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  12. #12
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    Okay thank you now I just need the final question
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