Answer:
An adult ticket costs £7.
A child ticket costs £2.
Step-by-step explanation:
Let a represent the cost for adults and let c represent the cost for children.
Family 1 has a total of 2 adults and 3 children. Together, it cost them £20.
In an equation, this is:
[tex]2a+3c=20[/tex]
Family 2 has a total of 1 adult and 4 children. It cost them £15. In an equation, this is:
[tex]a+4c=15[/tex]
We know have a system of equations. Solve it. We can use the substitution method.
First, subtract both sides by 4c in the second equation:
[tex]a+4c=15\\a=15-4c[/tex]
Substitute this into the first equation:
[tex]2a+3c=20\\2(15-4c)+3c=20[/tex]
Distribute:
[tex]30-8c+3c=20[/tex]
Add:
[tex]30-5c=20[/tex]
Subtract 30 from both sides. The left cancels:
[tex]-5c=-10[/tex]
Divide both sides by -5:
[tex](-5c)/-5=(-10)/-5\\c=2[/tex]
Thus, the cost of a child ticket is £2.
Substitute 2 for c into the equation we manipulated at the start:
[tex]a=15-4c\\a=15-4(2)\\a=15-8=7[/tex]
Thus, the cost of an adult ticket is £7.
