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Math Help - price of popcorn, drink and crisps

  1. #1
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    price of popcorn, drink and crisps

    So friends go to the cinema and buy 1 large tub of popcorn, 4 fizzy drinks and 10 packets of crisps. The bill comes to 10.89
    Some other friends go to the cinema and buy 1 large tub of popcorn, 3 fizzy drinks and 7 packets of crisps. The bill comes to 8.64

    How much is 1 large tub of popcorn, 1 fizzy drink and 1 packet of crisps?

    I got:

    1P + 4D + 10C = 10.89
    1P + 3D + 7D = 8.64

    When I subtract one from the other I get: 1D + 3C = 2.25

    How do I get the prices for 1 large tub of popcorn, 1 fizzy drink and 1 packet of crisps from there??

    Many thanks for any help.
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  2. #2
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    Re: price of popcorn, drink and crisps

    Quote Originally Posted by Natasha1 View Post
    So friends go to the cinema and buy 1 large tub of popcorn, 4 fizzy drinks and 10 packets of crisps. The bill comes to 10.89
    Some other friends go to the cinema and buy 1 large tub of popcorn, 3 fizzy drinks and 7 packets of crisps. The bill comes to 8.64

    How much is 1 large tub of popcorn, 1 fizzy drink and 1 packet of crisps?

    I got:

    1P + 4D + 10C = 10.89
    1P + 3D + 7D = 8.64

    When I subtract one from the other I get: 1D + 3C = 2.25

    How do I get the prices for 1 large tub of popcorn, 1 fizzy drink and 1 packet of crisps from there??

    Many thanks for any help.
    You can't pay fractions of a pence.

    Are you sure there isn't more to this problem? I'm getting a lot of solutions.
    Last edited by romsek; December 23rd 2013 at 03:14 AM.
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  3. #3
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    Re: price of popcorn, drink and crisps

    1P + 4D + 10C = 1089
    1P + 3D + 7D = 864

    When I subtract one from the other I get: 1D + 3C = 225
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  4. #4
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    Re: price of popcorn, drink and crisps

    yes. And that gives you a line of possible solutions. I'm showing 74 valid solutions total.
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  5. #5
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    Re: price of popcorn, drink and crisps

    May I have a hint in terms of finishing this problem as I don't know what to do next?
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  6. #6
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    Re: price of popcorn, drink and crisps

    Quote Originally Posted by Natasha1 View Post
    So friends go to the cinema and buy 1 large tub of popcorn, 4 fizzy drinks and 10 packets of crisps. The bill comes to 10.89
    Some other friends go to the cinema and buy 1 large tub of popcorn, 3 fizzy drinks and 7 packets of crisps. The bill comes to 8.64

    How much is 1 large tub of popcorn, 1 fizzy drink and 1 packet of crisps?

    I got:

    1P + 4D + 10C = 10.89
    1P + 3D + 7D = 8.64
    It would be a good idea to state "P is the cost of 1 large tub of popcorn, D is the cost of one fizzy drink, and C is the cost of one packet of crisps". Also, you mean "7C", not "7D". Other than that, yes, those are the two equations.

    When I subtract one from the other I get: 1D + 3C = 2.25

    How do I get the prices for 1 large tub of popcorn, 1 fizzy drink and 1 packet of crisps from there??

    Many thanks for any help.
    From D+ 3C= 2.25, you have D= 2.25- 3C. Putting that into P+ 4D+ 10C= 10.89, we have P+ 4(2.25- 3C)+ 10C= P+ 9.00- 12C+ 10C= 10.89 so that P- 2C= 1.89 and then P= 2C+ 1.89.

    Since you have only two equations with three unknown values, this is the best you can do: write P and D in terms of C. Of course, since, as romsek said, the prices must be integer numbers of pence, you could start with C= 0.01, C= 0.02, .... and increase from there.
    Thanks from Natasha1
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  7. #7
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    Re: price of popcorn, drink and crisps

    Hello, Natasha1!

    1 popcorn, 4 drinks and 10 crisps cost $10.89.
    1 popcorn, 3 drinks and 7 crisps cost $8.64.

    How much is 1 popcorn, 1 drink and 1 crisp?

    We have: . \begin{Bmatrix}P + 4D + 10C &=& 10.89 & [1]\\ P + 3D + 7C &=& 8.64 & [2] \end{Bmatrix}

    Subtract [1] - [2]: . D + 3C \:=\:2.25 \quad\Rightarrow\quad D \:=\:2.25 - 3C


    Substitute into [1]: . P + 4(2.25-3C) + 10C \:=\:10.89

    . . . P + 9 - 12C + 10C \:=\:10.89 \quad\Rightarrow\quad P \:=\:1.89 + 2C


    \begin{array}{cccccc}\text{We have:} & P &=& 1.89 + 2C \\ & D & =& 2.25 - 3C \\ & C &=& C \end{array}


    Add: . P + D + C \;=\;4.14
    Thanks from Natasha1 and sakonpure6
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  8. #8
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    Re: price of popcorn, drink and crisps

    Want a beautifully well explained solution. Thanks Soroban!
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  9. #9
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    Re: price of popcorn, drink and crisps

    [deleted]
    Last edited by romsek; December 23rd 2013 at 11:34 AM.
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  10. #10
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    Re: price of popcorn, drink and crisps

    I'm sorry Romsek, I only wrote the problem as it was written to me... apologies.
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  11. #11
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    Re: price of popcorn, drink and crisps

    I shouldn't have ragged on you which is why I deleted the post. No worries.
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