# price of popcorn, drink and crisps

• Dec 23rd 2013, 02:52 AM
Natasha1
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.
• Dec 23rd 2013, 03:58 AM
romsek
Re: price of popcorn, drink and crisps
Quote:

Originally Posted by Natasha1
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.
• Dec 23rd 2013, 04:11 AM
Natasha1
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
• Dec 23rd 2013, 04:31 AM
romsek
Re: price of popcorn, drink and crisps
yes. And that gives you a line of possible solutions. I'm showing 74 valid solutions total.
• Dec 23rd 2013, 04:46 AM
Natasha1
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?
• Dec 23rd 2013, 05:24 AM
HallsofIvy
Re: price of popcorn, drink and crisps
Quote:

Originally Posted by Natasha1
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.

Quote:

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.
• Dec 23rd 2013, 07:59 AM
Soroban
Re: price of popcorn, drink and crisps
Hello, Natasha1!

Quote:

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: . $P + D + C \;=\;4.14$
• Dec 23rd 2013, 08:20 AM
Natasha1
Re: price of popcorn, drink and crisps
Want a beautifully well explained solution. Thanks Soroban!
• Dec 23rd 2013, 12:01 PM
romsek
Re: price of popcorn, drink and crisps
[deleted]
• Dec 23rd 2013, 04:58 PM
Natasha1
Re: price of popcorn, drink and crisps
I'm sorry Romsek, I only wrote the problem as it was written to me... apologies.
• Dec 23rd 2013, 05:03 PM
romsek
Re: price of popcorn, drink and crisps
I shouldn't have ragged on you which is why I deleted the post. No worries.