Question

A group of 40 people attended a ball game. There were three times as many children as adults in the group. Set up a system of equations that represents the numbers of adults and children who attended the game and solve the system to find the number of children who were in the group.

A. 30 adults, 10 children
B. 10 adults, 30 children
C. 19 adults, 21 children
D. 21 adults, 19 children

Answer 1

To set up a system of equations to represent the numbers of adults and children who attended the game, we can use the information given: Let's assume that the number of adults is A and the number of children is C. From the given information, we can write two equations and solve the system to find the number of children who were in the group.

Step-by-step explanation:

To set up a system of equations to represent the numbers of adults and children who attended the game, we can use the information given:

Let's assume that the number of adults is A and the number of children is C.

From the given information, we can write the following equations:

Equation 1: C = 3A (There were three times as many children as adults)

Equation 2: A + C = 40 (A group of 40 people attended the game)

Now, we can solve this system of equations:

Substituting the value of C from Equation 1 into Equation 2:

A + 3A = 40

4A = 40

A = 10

Substituting the value of A into Equation 1:

C = 3(10)

C = 30

Therefore, there were 10 adults and 30 children in the group.