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+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.