Final answer:
To find the cost of an adult movie ticket, we can set up a system of equations using the given information. By solving the system of equations, we find that the cost of an adult movie ticket is $20.00.
Step-by-step explanation:
To find the cost of an adult movie ticket, we can set up a system of equations using the given information. Let's assign the cost of an adult movie ticket as 'x.'
From the first scenario, we know that 2x + 4y = 64, where x is the cost of an adult ticket and y is the cost of a child ticket.
From the second scenario, we know that 2x + 6y = 84.
Now, we can solve these equations simultaneously to find the value of x, which represents the cost of an adult movie ticket.
Multiplying the first equation by 3 and the second equation by 2 will allow us to eliminate the x term when subtracting the two equations.
After subtracting these two equations, we are left with 2y = 12. Solving for y, we find that y = 6.
Substituting this value of y back into either of the original equations, we can solve for x. Plugging in y = 6 in the first equation, we get 2x + 4(6) = 64. Simplifying this equation, we find that 2x + 24 = 64. Subtracting 24 from both sides, we get 2x = 40. Dividing both sides by 2, we find that x = 20.
Therefore, the cost of an adult movie ticket is $20.00.