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
11 Feb 23
@venda saidSo your first trip must break down something like this -
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
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.
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.
12 Feb 23
@orangutan saidThe published answer is much simpler ,although your answer may be correct as well
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 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