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[Solved] Equation problem

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Tickets for an ice-skating display are sold at $5 for adults and $2 for children. If 101 tickets were sold altogether for a take of $394, find the number of adults and children who attended.

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Let \small a denote the number of adults and \small c the number of children. We are told that 101 tickets were sold so we must have 

\small a+c=101     (1)

We are also told that 

\small 5a+2c=394  (2)

To solve this set of equations multiply equation (1) by 5 to get

  \small 5a+5c=505   (3)

\small 5a+2c=394    (2)

Do equation(3) - equation (2) to get

\small 5a-5a+5c-2c=505-394=3c=111\Rightarrow c=37.

That is, 64 adults and 37 children attended the display.

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