Answer:
One adult ticket costs £9.25, and one child ticket costs £6.25.
Explanation:
Let a = price of 1 adult ticket.
Let c = price of 1 child ticket.
"A family of two adults and four children pay £43.50. for entry."
2a + 4c = 43.5
"Another family of five adults and three children pay £65."
5a + 3c = 65
We have a system of simultaneous equation in two unknowns.
2a + 4c = 43.5
5a + 3c = 65
Let's solve the system by the method of elimination. We need to add multiples of the two equations in a way that one variable will be eliminated (add to zero).
Let's eliminate the variable a. Multiply both sides of the first equation by -5 Multiply both sides of the second equation by 2. Then add them.
-10a - 20c = -217.5
+ 10a + 6c = 130
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-14c = -87.5
c = 6.25
Now substitute 6.25 for c in the first original equation and solve for a.
2a + 4c = 43.5
2a + 4(6.25) = 43.5
2a + 25 = 43.5
2a = 18.5
a = 9.25
Answer: One adult ticket costs £9.25, and one child ticket costs £6.25.