A group of 45 people attended a ball game. There were twice 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.

Question

A group of 45 people attended a ball game. There were twice 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+c=45 c=2a;15 adults,30 children
a+c=45 a=c+2;30 adults;22 children
a+c=45 c=a+2; 22 adults;30 children
a+c=45 a+2c; 30 adults;15 children

Answer 1

The correct system of equations would be:

a + c = 45
c = 2a

To solve this system, you can substitute the second equation into the first equation:

a + 2a = 45
3a = 45
a = 15

Then, you can substitute the value of a back into the second equation to find the value of c:

c = 2(15)
c = 30

Therefore, there were 30 children in the group.

Answer 2

Let's set up a system of equations to represent the numbers of adults and children who attended the game.

Let a represent the number of adults and c represent the number of children.

We know that there were twice as many children as adults, so we can set up the equation c = 2a.

We also know that the total number of people who attended the game was 45, so we can set up the equation a + c = 45.

Now, we can solve the system of equations to find the number of children who were in the group.

Using the equation c = 2a, we substitute 2a in place of c in the second equation:

a + 2a = 45

Combining like terms, we get:

3a = 45

Dividing both sides by 3, we get:

a = 15

Now, substituting the value of a into the equation c = 2a, we get:

c = 2 * 15

c = 30

Therefore, there were 30 children in the group.

Answer 3

To set up a system of equations representing the number of adults and children in the group, we can use the following information:

1. There were 45 people in total.
2. There were twice as many children as adults.

Let's start by defining our variables. Let a represent the number of adults and c represent the number of children in the group.

From the first piece of information, we can form the equation:
a + c = 45

From the second piece of information, we can form the equation:
c = 2a

Now we have a system of equations:
1. a + c = 45
2. c = 2a

To solve this system, we can substitute equation 2 into equation 1. This means we replace c in equation 1 with 2a:

a + 2a = 45

Combining like terms, we get:
3a = 45

Now we can solve for a by dividing both sides of the equation by 3:
a = 45 / 3
a = 15

Now that we have the value of a, we can substitute it back into equation 2 to find the value of c:
c = 2a
c = 2 * 15
c = 30

Therefore, there were 15 adults and 30 children in the group.