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Math Help - Another word problem

  1. #1
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    Another word problem

    The sum of two numbers is 42. One number plus two times the other number is 57. What are the two numbers?

    I need the formula as well to help me learn to disect these problems. I have a block or something. Is there an easy way to learn this!!!! Age problems are worse!
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  2. #2
    Site Founder Math Help's Avatar
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    words to equations

    try to write mathematical equations from the information provided.
    Let us call 1 of the numbers x and the other y. now try to do it and I will correct you.
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  3. #3
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    This is the formula I think. I just don't know how to solve it without
    more information


    x+2y=42
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  4. #4
    Site Founder Math Help's Avatar
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    2 equations 2 unknowns

    Quote Originally Posted by Nicv
    The sum of two numbers is 42.
    x + y = 42
    Quote Originally Posted by Nicv
    One number plus two times the other number is 57..
    x + 2y = 57

    can you take it from here?
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  5. #5
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    Nope, sorry.
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  6. #6
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    OK, no problem,

    First is important that you understand where these equations come from.

    x + y = 42
    x + 2y = 57

    Once you understand how I wrote these equations from the given information we can solve this system of equations using substitution or subtracting the top equation from the bottom and then using substitution.

    ..(x + 2y = 57)
    -(x + y = 42)
    ........y = 15

    now plug in y=15 into either equation above and solve for x. Give it a try and I will correct you if you make a mistake.
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  7. #7
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    that totally makes sense now. what happens in this case?

    x-y=80
    3x=4y=-334

    i appreciate your help. i am taking an online course and this self teaching isn't
    really working for me. no worries i don't hand any of this in!
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  8. #8
    Site Founder Math Help's Avatar
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    2 equations 2 unknowns

    x-y=80
    3x+4y=-334

    Lets solve for x in terms of y on the first equation and then plug it in to the second.

    x-y=80
    x=y+80 eq1

    3x+4y=-334 (plug in eq1 for x)
    3(y+80)+4y=-334
    3y+240+4y=-334
    7y=-574
    y=-82

    now plug in y to the first equation
    x-(-82)=80
    x=-2
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  9. #9
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    Here is one way.

    "The sum of two numbers is 42. One number plus two times the other number is 57. What are the two numbers?"

    Let x = one number
    So, 42-x is the other number

    x +2(42-x) = 57
    x +84 -2x = 57
    x -2x = 57 -84
    -x = -27
    x = 27

    42-x = 42-27 = 15

    Therefore, the two numbers are 15 and 27. ----answer.

    ----------------
    Another way.

    Let x = one number
    And y = the other number

    x +y = 42 ----(i)
    x +2y = 57 ----(ii)

    From (i), x = 42-y
    Substitute that into (ii),
    (42-y) +2y = 57
    42 -y +2y = 57
    -y +2y = 57 -42
    y = 15

    So,
    x = 42-y = 42-15 = 27

    Therefore, the two numbers are 15 and 27.

    Or,
    (ii) minus (i),
    y = 15 ----right away.
    etc...
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