52 people attend a ball game...

[BossanovaFiend]

I'm stuck again...
The last one I sort of figured out on my own but this one I've been working on for a really long time now and I have no idea what I'm doing. :

A group of 52 attend a ball game. There were three times as many children as adults in the group. Write a system of equations that you could use to set up this problem, where a is the number of adults and c is the number of children in the group.
Solve the system of equations for c, the number of children in the group.

 

[soroban]

Hello, BossanovaFiend!

A group of 52 attend a ball game.
There were three times as many children as adults in the group.

Write a system of equations that you could use to set up this problem,
where \(\displaystyle a\) is the number of adults and \(\displaystyle c\) is the number of children in the group.
Solve the system of equations for \(\displaystyle c\), the number of children in the group.

Let \(\displaystyle a\) = number of adults.
Let \(\displaystyle c\) = number of children.


\(\displaystyle \text{"A group of 52 attend a ball game": }\;a + c \:=\:52\)

\(\displaystyle \text{"Three times as many children as adults: }\;c \:=\;3a\)


\(\displaystyle \text{There is your system of equations: }\;\begin{array}{ccc}a + c &=& 52 \\ 3a - c &=& 0 \end{array}\)

 

[BossanovaFiend]

Thanks so much!!