Adult tickets to a play cost $22. Tickets for children cost $15. Tickets for a group of 11 people cost a total of $228. Write and solve a system of equations to find how many children and how many adults were in the group.

Question

Adult tickets to a play cost $22. Tickets for children cost $15. Tickets for a group of 11 people cost a total of $228. Write and solve a system of equations to find how many children and how many adults were in the group.

A. 2 children, 9 adults
B. 4 children, 7 adults
C. 5 children, 6 adults
D. 7 children, 4 adults

Answer 1

a + c = 11 ----> c = 11-a

22a + 15c = 228
sub c = 11-a into this equation
22a + 15(11-a) = 228

solve this equation for a, then sub into c = 11-a

or...

you could just test each of the given answers.

Answer 2

Let's use a system of equations to solve this problem.

Let's assume that the number of child tickets is represented by 'c', and the number of adult tickets is represented by 'a'.

From the given information, we can set up two equations:

Equation 1: c + a = 11 (since the total number of people in the group is 11)

Equation 2: 15c + 22a = 228 (since the total cost of the tickets for the group is $228)

To solve this system of equations, we can use the substitution method.

First, let's solve Equation 1 for 'c':

c = 11 - a

Now substitute this value of 'c' into Equation 2:

15(11 - a) + 22a = 228

Distribute the 15:

165 - 15a + 22a = 228

Combine like terms:

165 + 7a = 228

Subtract 165 from both sides:

7a = 63

Divide both sides by 7:

a = 9

Now substitute this value of 'a' back into Equation 1 to find 'c':

c + 9 = 11

c = 2

So, there are 2 children and 9 adults in the group.

Therefore, the correct answer is:

A. 2 children, 9 adults

Answer 3

Let's assume the number of children in the group is c and the number of adults is a.

We know that an adult ticket costs $22 and a child ticket costs $15. So, we can set up the following equations:

22a + 15c = 228 ... (1) (equation representing the total cost of all tickets)
a + c = 11 ... (2) (equation representing the total number of people in the group)

To solve this system of equations, we can use the method of substitution or elimination.

Let's use the method of substitution.

Rearrange equation (2) to get c = 11 - a.

Substitute this expression for c in equation (1):

22a + 15(11 - a) = 228

Simplify and solve for a:

22a + 165 - 15a = 228
7a + 165 = 228
7a = 228 - 165
7a = 63
a = 63/7
a = 9

Now, substitute this value of a back into equation (2) to find c:

9 + c = 11
c = 11 - 9
c = 2

Therefore, there were 2 children and 9 adults in the group.

So, the correct answer is A. 2 children, 9 adults.