Few quick math problems

Discussion in 'General Discussions' started by unknown2, May 13, 2007.

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  1. unknown2

    unknown2 Level IV

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    Ok, so I completely forget all of these, lol, it's sad, just did them a few years ago.

    1. Solve the following systme of linear equations.
    4x + 3y = 13
    5x + y - 8 = 0

    2.An apartment building has 80 units. 1 bedroom for $850, 2 bedroom for $1050. The monthly income is 78 400$. How many of each type are there?

    3.explain the steps to use the elimination method for the following:

    5x + 2y = 5
    3x - 4y = -23

    4. three bricklayers and 4 carpenters earn $910 per day. 10 bricklayers and 5 carpenters earn 1850$ a day

    a) set up a system of equations
    b) is there an advantage to eliminating either variable first?
    c) determine the daily wage of the bricklayer

    5. tickets are sold for 7$ in advance and $9.50 at the door. 300 tickets were sold for a total of $2405.00. How many of each were sold?

    Thanks, if somebody could help explain the steps for these, it would help.
     
  2. lazypando

    lazypando Level IV

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    o1.
    x = 1
    y = 3
    Code (Text):
    1. 4x + 3y = 13
    2. 5x + y - 8 = 0
    3.  
    4. get rid of the y variable by multiplying the second equation by -3
    5. 4x + 3y = 13
    6. -15x + -3y + 24 = 0
    7.  
    8. add the two equations together
    9. -11x + 24 = 13
    10.  
    11. move the 24 to the right side
    12. -11x = -11
    13.  
    14. solve
    15. x = 1
    16.  
    17. substitute x into the first equations
    18. 4(1) + 3y = 13
    19. 3y = 9
    20. y=3
    o2.
    1 bedroom = 28
    2 bedroom = 52
    Code (Text):
    1. x = 1 bedroom
    2. y = 2 bedroom
    3.  
    4. two equations
    5. x + y = 80
    6. 850x + 1050y = 78400
    7.  
    8. solve the first equation for y
    9. y = 80 - x
    10.  
    11. substitute into the second equation
    12. 850x + 1050(80 - x) = 78400
    13.  
    14. simplify
    15. -200x + 84000 = 78400
    16.  
    17. solve
    18. -200x = -5600
    19. x = 28
    20.  
    21. substitute into the first equation
    22. x + y = 80
    23. 28 + y = 80
    24. y = 52
    o3.
    Code (Text):
    1. multiply the first equation by 2
    2. 10x + 4y = 10
    3. 3x - 4y = -23
    4.  
    5. add the two equations together
    6. 13x = -13
    7.  
    8. solve
    9. x = -1
    10.  
    11. substitute x into first equation
    12. 10(-1) + 4y = 10
    13. 4y -10 = 10
    14. 4y = 20
    15. y = 5
    o4.
    Code (Text):
    1. x = bricklayer
    2. y = carpenter
    3.  
    4. a) set up a system of equations
    5. 3x + 4y = 910
    6. 10x + 5y = 1850
    7.  
    8. b) is there an advantage to eliminating either variable first?
    9. not that I see...but since question c asks to find the wage of a bricklayer, I'd eliminate y first so I don't have to solve for both x and y...
    10.  
    11. c) determine the daily wage of the bricklayer
    12. multiply the first equation by -5 and the second by 4
    13. -15x - 20y = -4550
    14. 40x + 20y = 7400
    15.  
    16. add the two equations together
    17. 25x = 2850
    18.  
    19. solve
    20. x = 114
    o5.
    tickets sold in advance = 178
    tickets sold at the door = 122
    Code (Text):
    1. x = ticket sold in advance
    2. y = ticket sold at the door
    3.  
    4. two equations
    5. x + y = 300
    6. 7x + 9.5y = 2405
    7.  
    8. solve the first equation for y
    9. y = 300 - x
    10.  
    11. substitute into the second equation
    12. 7x + 9.5(300 - x) = 2405
    13.  
    14. simplify
    15. -2.5x + 2850 = 2405
    16.  
    17. solve
    18. -2.5x = -445
    19. x = 178
    20.  
    21. substitute x into the first equation
    22. 178 + y = 300
    23. y = 122
    NOTE : tac123 finished problems 2-5 before me so all credit goes to him/her...
     
  3. SoC

    SoC Moderator
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    1. Solve the following systme of linear equations.
    4x + 3y = 13
    5x + y - 8 = 0


    5x + y = 8

    x 3

    15x + 3y = 24
    4x+3y=13

    take em away from each other

    11x = 11.

    X = 1. Then put 1 into the equation. 4x + 3y = 13, 4x = 4 + ?? = 13, Therfore 3y = 9 so y = 3.


    x = 1 || y = 3

    (ill look at others later :))

    Damn you lazypando :p
     
  4. tac123

    tac123 Level I

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    | 5 1 8 |
    | 4 3 13 |

    1 -2 -5
    4 3 13

    1 -2 -5
    0 11 33

    1 -2 -5
    0 1 3

    1 0 1
    0 1 3

    x = 1
    y = 3
    --------

    x + y = 80
    850*x + 1050*y = 78400

    1 1 80
    850 1050 78400

    1 1 80
    0 200 10400

    1 1 80
    0 1 52

    1 0 28
    0 1 52

    28 single bedroom, 52 doubles

    ------

    5x + 2y = 5
    3x - 4y = -23

    multiply first equation by 2
    10x + 4y = 10
    3x - 4y = -23

    add both equations
    13x + 0y = -13

    so x = -1

    substitute x into equation for y
    3(-1) - 4y = -23

    solve for y
    y = -20 / -4 = 5

    -----

    3 b + 4 c = 910
    10 b + 5 c = 1850

    b) trivial no matter which variable is eliminated first

    c)
    3 4 910
    10 5 1850

    3 4 910
    2 1 370

    1 3 540
    2 1 370

    1 3 540
    0 -5 -710

    1 3 540
    0 1 142

    1 0 114
    0 1 142

    brick layer has a wage of $114

    ---
    a + d = 300
    7 a + 9.5 d = 2405

    1 1 300
    7 9.5 2405

    1 1 300
    0 2.5 305

    1 1 300
    0 1 122

    1 0 178
    0 1 122

    advanced sales 178 tickets
    door sales 122 tickets


    Same steps as the problems above
     
  5. tac123

    tac123 Level I

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    Edit: Sorry for the double post, I can't delete my own posts can i?
     
  6. lazypando

    lazypando Level IV

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    don't hate :p
     
  7. tac123

    tac123 Level I

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    I just don't think it is very fair, because i'm sure I started my problems before lazy panda, and I also finished before her. Except she posted when she only had 1 problem done, and then edited as she worked, so now she looks like she was faster than me :-(.

    If you look at the times she finished her first problem at 12:38, and i finished my last problem at 12:41. Oh well, now i know the posting strategy for next time. :twisted:
     
  8. onprogus

    onprogus Level IV

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    Quit whining. It's not like it was a competition :p
    The fact that you both got the same answers is a good thing regardless of who did it first.
     
  9. lazypando

    lazypando Level IV

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    yup yup...you had them done way before me...sorry
     
  10. tac123

    tac123 Level I

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    No they were done, but there were 2 things.

    On the first problem, I made one of the numbers 1 instead of a 3, so I figured I would change that for him so that it was exactly his problem instead of just an example problem.

    Also, on another problem I just wrote down the wrong final solution, so I edited that. The other two were just formatting changes.

    But my work was there. *exasperated* Fine, I think we should have an independent party setup a math contest, and then we can go head to head. :D
     
  11. lazypando

    lazypando Level IV

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    sure thing :p
    and I've added a disclaimer now ^^
     
  12. tac123

    tac123 Level I

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    Aww... you're too nice. You probably helped him more though, your answers are nicely formated and explained, I just used Gaussian elimination and you can't really display it as well when you write it online as when you do it by hand.
     
  13. lazypando

    lazypando Level IV

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    there is a solution to that :p... it takes a bit more time but turns out nicely formated...just download MathEQ Expression Editor and upload the images...
     
  14. unknown2

    unknown2 Level IV

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    wow thanks guys :), hopefully i can do my 6 pages of HW now :p
     
  15. ChongChan

    ChongChan Level I

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    O M G what the hell is wrong with schools and collage. they are giving us HW like hell....!!!
     
  16. pandahorde

    pandahorde Level IV

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    if you study hard on algebra's or college math.. im sure you will love it.
    and im get ready on that..next 2 weeks is my 1st college life.[/code]
     
  17. btboy5

    btboy5 Level II

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    Wow, looks like there are some Mathematics experts here. If I have Differentiation and Integration problems I know who to look for now. :p
     
  18. Frozshtaliar

    Frozshtaliar Level II

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    lol im glad im done with math completely in college
     
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