Hint
This is quite a tricky puzzle, and knowledge of algebra would certainly help.
Answer
The children tickets were £14, and the adult tickets were £18.
Reasoning
There are a number of methods for solving this problem, including:
Using a spreadsheet.Using a computer program.Using the intersection of lines on a graph.Using an online equation solver.Solving simultaneous equations using algebra.Solving simultaneous equations using inverse matrices.
Here is my solution using simultaneous equations and algebra.
First construct two algebraic equations, where 'c' is the number of children, and 'a' is the number of adults:
4296c + 2143 x 18 = 98718 4296c + 38574 = 98718 4296c = 60144 c = 14
Double-Checking
c = 14 and a = 18
4,296 x 14 + 2,143 x 18 = 98,718
and
5,146 x 14 + 2,807 x 18 = 122,570
??
Puzzle 3
My first is in camel, and in hamster.
My second is in otter, but not in ferret.
My third is in mustang, but not in horse.
My fourth is in snake, and in asp.
My last is in tiger, and in panther.
Reasoning
My first is in camel, and in hamster = AEM
My second is in otter, but not in ferret = O
My third is in mustang, but not in horse = AGMNTU
My fourth is in snake, and in asp = AS
My last is in tiger, and in panther = ERT
??
Puzzle 4
How many people must be at a party before you are likely to have two having the same birthday (but not necessarily the same year)?
Reasoning
By likely, we mean greater than 50% chance.
With one person there is a 0 percent chance that you'll have two people with the same birthday.
With two people the probability that they won't share a birthday is 364 ÷ 365. The probability that they will share a birthday is therefore 1 − (364 ÷ 365).
With three people the probability that they won't share a birthday is the same as for two people, times 363 ÷ 365. So the probability that three people will share a birthday is 1 − (364 ÷ 365) x (363 ÷ 365).
Notice that with each additional person added, the probability that they share a birthday with one of the previous persons goes up, because there are fewer "free" days remaining.
We keep adding people until the percentage is greater than 50%.