newspaper puzzle part 2

newspaper puzzle part 2

Posers and Puzzles

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Dave

S.Yorks.England

Joined
18 Apr 10
Moves
84362
05 Feb 23

My local cafe sells only 2 items,but it's great value because you can buy one of each for only £2.I treated my friends and myself to one thing from each menu.We spent a total of £7 on pizza's and £9 on burgers.The next week we returned and everyone ordered something different.The bill was 4 times more expensive.
How much does a pizza cost

ook

hirsute rooster

Joined
13 Apr 05
Moves
20542
11 Feb 23

@venda said
My local cafe sells only 2 items,but it's great value because you can buy one of each for only £2.I treated my friends and myself to one thing from each menu.We spent a total of £7 on pizza's and £9 on burgers.The next week we returned and everyone ordered something different.The bill was 4 times more expensive.
How much does a pizza cost
So your first trip must break down something like this -
n1 * p = 7
n2 * b = 9
p + b = 2

If the bill then quadruples when everyone swaps their orders
then:
(n1 * b ) + (n2 * p) = 64

I then made an assumption that you have an integer number of friends (no fractional mates along for the pizza and burger fest).
I reasoned thusly -
If the burger bill on the first trip was £9 and given that a pizza and a burger only cost £2 together, then there can be only 5 or 6 people ordering burgers on the first trip (otherwise if there's more you need fractional pennies and if less then the burger is more than £2).
5 burgers @ £1.80 .. implying 20p for a pizza
6 burgers @ £1.50 .. implying 50p for a pizza

n1 * .2 = 7 ... n1 = 35
n2 * 1.8 = 9 ... n2 = 5

or

n1 * .5 = 7 ... n1 = 14
n2 * 1.5 = 9 ... n2 = 6

The first of these sets gives the second bill as £64 while the second solution yields only £21.

So the first is correct - you have 39 mates and a pizza costs 20p.

Please tell me the location of this cafe. All that working out has made me hungry.

Dave

S.Yorks.England

Joined
18 Apr 10
Moves
84362
12 Feb 23

@orangutan said
So your first trip must break down something like this -
n1 * p = 7
n2 * b = 9
p + b = 2

If the bill then quadruples when everyone swaps their orders
then:
(n1 * b ) + (n2 * p) = 64

I then made an assumption that you have an integer number of friends (no fractional mates along for the pizza and burger fest).
Hidden content removed
The published answer is much simpler ,although your answer may be correct as well
the initial constraints means a pizza costs 20p,50p,£1,£1.40 or £1.75 and the last one is the only one that quadruples the bill

ook

hirsute rooster

Joined
13 Apr 05
Moves
20542
13 Feb 23

@venda said
The published answer is much simpler ,although your answer may be correct as well
Hidden content removed
I still need to know where this cafe is ...
You and your mates are invited and we'll all have pizza.