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A total of 330 children and adults attended a school play. There were 21 times as many children in attendance as there were adults. ​ This situation is modeled by the given system of equations, where a represents the number of adults and c represents the number of children. ​ c=12a+c=330 ​ ​How many children attended the play?​

Respuesta :

Answer: 315 children attended the play.

Step-by-step explanation:

Let c represent the number of children that attended the play.

Let a represent the number of adults that attended the play.

A total of 330 children and adults attended the school play. It means that

c + a = 330 - - - - - - - - - -1

There were 21 times as many children in attendance as there were adults. It means that

c = 21a

Substituting c = 21a into equation 1, it becomes

21a + a = 330

22a = 330

a = 330/22

a = 15

Substituting a = 15 into c = 21a, it becomes

c = 21 × 15

c = 315

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