Using a System of Equations

A total of 300 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 = 21a
a + c = 330

How many children attended the play?

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Use the given system of equations to solve for c, the number of children attending.

c = 21a
a + c = 330

a + 21a = 330   {substituted 21a, in for c, into second equation}
22a = 330    {combined like terms}
a = 15   {divided each side by 22}

15 adults attended

c = 21a   {first original equation}
c = 21(15)   {substituted 15, in for a, into first equation}
c = 315   {multiplied}

315 children attended

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