Answer:
Cost of an adult ticket is £10.75
Step-by-step explanation:
Given:-
Cost of 1 adult ticket is £6 more that the cost of a child ticket.
Total cost of 6 tickets = £40.50
c is cost of a child ticket and a is the cost of an adult ticket.
To find:- Cost of 1 adult ticket =?
Solution:-
For 2 adults and 4 children, and the total cost of tickets is £40.5, we get the following equation,
[tex]2a+4c=40.5[/tex] -----------------(1)
As the Cost of 1 adult ticket is £6 more than the cost of a child ticket, we can the following equation,
[tex]a=c+6[/tex] -----------------(2)
Now, substituting the value of a from equation 2 in equation 1 we get,
[tex]2a+4c=40.5[/tex]
[tex]2(c+6)+4c=40.5[/tex]
[tex]2c+12+4c=40.5[/tex]
[tex]6c=40.5-12[/tex]
[tex]6c=28.5[/tex]
[tex]c=\frac{28.5}{6}[/tex]
[tex]c=4.75[/tex] --------------------(3)
Now substituting the value of c from equation 3 in equation 2,
[tex]a=c+6[/tex]
[tex]a=4.75+6[/tex]
[tex]a=10.75[/tex]
As a is the cost of 1 adult ticket,
Therefore Cost of an adult ticket is £10.75
