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Math Help - setting up a system of equations

  1. #1
    EPZ
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    setting up a system of equations

    Q: Four large cheeseburgers and two chocolate shakes cost a total of $7.90. Two shakes cost 15 cents more than one cheeseburger. What is the cost of a cheeseburger? A shake?

    A: I will let x=cost of cheeseburger and y=cost of shake. We know that four large cheesbeburgers and two chocolates shakes costs a total of $7.90; thus, our first equation is 4x+2y=7.90. Now, we also know that two shakes cost 15 cents more than one cheeseburger. This implies, x-2y=0.15. So, the system of equations is,


    4x+2y=7.90
    x-2y=0.15.

    Therefore, x=$1.61 and y=$0.73.

    This is not the answer in the back of the book. I am not sure what I am doing wrong.

    I got the second question!

    Thanks
    Last edited by EPZ; December 31st 2009 at 03:50 PM.
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  2. #2
    Master Of Puppets
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    Quote Originally Posted by EPZ View Post


    4x+2y=7.90
    x-2y=0.15.
    try

     <br />
2y-x=0.15 <br />
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  3. #3
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    For the first one: let cheeseburgers = c, let shakes = s

    from the question:
    4c + 2s = 7.90 (1)
    2s = c + 0.15 (2)

    putting (2) into (1)

    4c + c + 0.15 = 7.90
    5c + 0.15 = 7.90
    5c = 7.75
    c = 7.75 / 5
    c = 1.55

    you should be able to get both prices from here...
    Last edited by Joel; December 31st 2009 at 03:56 PM. Reason: Error picked up by pickslides.
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  4. #4
    Master Of Puppets
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    Quote Originally Posted by Joel View Post
    For the first one: let cheeseburgers = c, let shakes = s

    from the question:
    4c + 2s = 7.90 (1)
    2s = c + 15 (2)
    be careful Joel, this system implies $15 is the difference


    Quote Originally Posted by Joel View Post
    5c + 15 = 7.90
    5c = 7.75
     <br />
7.90-15 = -7.10\neq 7.75<br />
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  5. #5
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    Q1.

    c=cheeseburge, s=shake.

    eq1. 4c+2s=7.9
    eq2. 2s-0.15=c
    Substitute eq2. into eq1.
    4(2s-0.15)+2s=7.9
    8s-0.6+2s=7.9
    10s=8.5
    s=0.85
    Substitute this into eq2.
    2(0.85)-0.15=c
    1.7-0.15=c
    c=1.55
    Check with eq1.
    4(1.55)+2(0.85)=7.9

    Q2.

    c=cashew, p=peanut, m=mixture w=weight

    eq1. c=5/w
    eq2. p=1.5/w
    eq3. 30p+xc=m(30+x)
    eq4. m=3/w
    Sustitute eq1,2,4. into eq3.
    30(1.5/w)+x(5/w)=(3/w)(30+x)
    Mutliply all by w (obviously as each weight was per lb).
    30(1.5)+x(5)=3(30+x)
    45+5x=90+3x
    2x=45
    x=22.5

    We need to ass 22.5 lb's of cashews.
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