Theater Total Value of Ticket Sales
A $1,600
B $2,000
C $1,800
D $4,800
E $3,200
The table above shows the total value of the ticket sales for an afternoon show in each of five movie theaters.
There were 300 tickets that were sold for each theater. The tickets cost $8 for each adult and $4 for each child.
In which theater was the number of children twice the number of adults?
If there is twice as many children multiply 4 by 2 to get 8 +8 adults =16 the answer should be know obvious.
x+y=300 where x = adults and y = children
you know that there are twice as many children as adults, therefore y=2x. plug this back into the equation.
x+2x=300 solve this to get x=100. plug this x value into the original equation x+y=300 and you get y=200. 100*8=800, the cost of 100 adult tickets. 200*4=800, the cost of 200 child tickets. total cost = 800+800=1600=A
To determine the theater in which the number of children was twice the number of adults, we need to calculate the number of adults and children in each theater.
Let's start by calculating the number of adults and children in each theater. Since the total number of tickets sold for each theater is 300, we can assume that the sum of adults and children is equal to 300.
Let's use variables to represent the number of adults and children in each theater. Let's say there are 'x' adults in each theater, and 'y' children.
So, the equation will be: x + y = 300
Now we need to determine the ticket sales for each theater. The cost of an adult ticket is $8, and the cost of a child ticket is $4.
The total value of ticket sales for each theater can be calculated by multiplying the number of adults by the cost of an adult ticket, and adding it to the product of the number of children and the cost of a child ticket.
For example, for theater A, the total value of ticket sales is given as $1,600. Since there were 300 tickets sold in each theater, we can set up the equation as follows:
8x + 4y = 1600
Similarly, we can set up equations for theaters B, C, D, and E based on the given total value of ticket sales.
By solving the system of equations, we can find the values of 'x' and 'y' for each theater. Then, we can check which theater has the number of children twice the number of adults.