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A group of 68 people 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.

chitsuii  Jul 3, 2018
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A group of 68 people 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.

 

Let a = adults
Let c = children

 

\(\begin{array}{|lrcll|} \hline (1) & a + c &=& 68 \\ & a &=& 68-c \\\\ (2) & c &=& 3a \quad & | \quad a = 68-c \\ & c &=& 3(68-c) \\ & c &=& 204-3c \quad & | \quad + 3c \\ & c+3c &=& 204 \\ & 4c &=& 204 \quad & | \quad : 4 \\ & \mathbf{ c} & \mathbf{=}& \mathbf{51} \\\\ & a &=& 68-c \\ & a &=& 68-51 \\ & \mathbf{a} & \mathbf{=}& \mathbf{17} \\ \hline \end{array} \)

 

The number of children in the group is 51

 

laugh

heureka  Jul 3, 2018

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