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The school that Tyson attends is selling tickets to a performance. On the first day ofticket sales the school sold 5 adult tickets and 2 child tickets for a total of $138.50. The school tookin $185.50 on the second day by selling 7 adult tickets and 2 child tickets. Find the price of an adultticket and the price of a child ticket.

User Gregsdennis
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1 Answer

7 votes
7 votes

Let a represent the cost of adult tickets and c represent the cost of children's tickets.

On the first day, $138.50 worth of tickets were sold by selling 5 adult tickets and 2 child tickets. This means that:


5a+2c=138.50

On the second day, $185.50 worth of tickets were sold by selling 7 adult tickets and 2 child tickets. This means that:


7a+2c=185.50

We can solve the simultaneous equations by subtracting the two equations:


\begin{gathered} 7a-5a+2c-2c=185.50-138.50 \\ 2a=47 \\ a=(47)/(2) \\ a=23.5 \end{gathered}

We can solve for c by substituting for a into the first equation:


\begin{gathered} 5(23.5)+2c=138.50 \\ 117.5+2c=138.50 \\ 2c=138.50-117.50=21 \\ c=(21)/(2) \\ c=10.5 \end{gathered}

Therefore, an adult ticket costs $23.50 and a child ticket costs $10.50.

User Scarhand
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