A group of adults and kids went to see a movie. Tickets cost $7.00 each for adults and $4.50 each for kids, and the group paid $64.00 in total. There were 4 fewer adults than kids in the group. Find the number of adults and kids.
To solve this problem, let's set up a system of equations.
Let's say the number of adults in the group is "A" and the number of kids is "K".
We know that the cost of one adult ticket is $7, so the total cost of adult tickets would be 7A.
Similarly, the cost of one kid's ticket is $4.50, so the total cost of kids' tickets would be 4.50K.
We are also given that the group paid a total of $64 for the tickets. Therefore, the equation for the total cost is:
7A + 4.50K = 64
We are also told that there were 4 fewer adults than kids in the group, so we can write another equation:
A = K - 4
Now we have a system of equations:
7A + 4.50K = 64 (Equation 1)
A = K - 4 (Equation 2)
We can solve this system of equations to find the values of A and K.
To eliminate A, we can substitute the value of A from Equation 2 into Equation 1:
7(K - 4) + 4.50K = 64
7K - 28 + 4.50K = 64
11.5K = 92
K = 8
Now that we know the value of K, we can substitute it back into Equation 2 to find the value of A:
A = 8 - 4
A = 4
Therefore, there are 4 adults and 8 kids in the group.
you know:
7a+4.5c = 64
a = c-4
now just solve for a and c.