A group of 16 people bought tickets to a museum. They paid a total of $56. Each adult ticket costs $4 and each child ticket costs $2. Formulate and solve a system of equations to determine how many adult tickets and child tickets did they buy.
Responses
A 4 adult tickets, 12 child tickets4 adult tickets, 12 child tickets
B 8 adult tickets, 8 child tickets8 adult tickets, 8 child tickets
C 10 adult tickets, 6 child tickets10 adult tickets, 6 child tickets
D 12 adult tickets, 4 child tickets
Let's assume x as the number of adult tickets and y as the number of child tickets.
From the information given, we can form two equations:
Equation 1: x + y = 16 (The total number of people is 16)
Equation 2: 4x + 2y = 56 (The total cost of the tickets is $56)
Now we can solve this system of equations.
Multiply Equation 1 by 2 to make the coefficients of y equal:
2(x + y) = 2(16)
2x + 2y = 32
Subtract this equation from Equation 2 to eliminate y:
4x + 2y - 2x - 2y = 56 - 32
2x = 24
x = 12
Substitute x = 12 into Equation 1 to find the value of y:
12 + y = 16
y = 4
Therefore, they bought 12 adult tickets and 4 child tickets.
The answer is D: 12 adult tickets, 4 child tickets.
You are planning to take a group of friends to the movies for your birthday. The local movie theater charges $12.99 per person. When you check the company's website, you find that they also offer a special group rate. The group rate is only $8.99 per person but also includes a $20 reservation fee in addition to the cost per person.
What is the maximum number of people that could attend your party in order for the individual admission rate to be a better deal?
Responses
A 2 people2 people
B 3 people3 people
C 4 people4 people
D 5 people5 people
E 6 people