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.

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.

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

Re: price of popcorn, drink and crisps

yes. And that gives you a line of possible solutions. I'm showing 74 valid solutions total.

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?

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.

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

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

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

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

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

Add: .$\displaystyle P + D + C \;=\;4.14$

Re: price of popcorn, drink and crisps

Want a beautifully well explained solution. Thanks Soroban!

Re: price of popcorn, drink and crisps

Re: price of popcorn, drink and crisps

I'm sorry Romsek, I only wrote the problem as it was written to me... apologies.

Re: price of popcorn, drink and crisps

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