Question

850 tickets were sold for a game for a total of $1,512.50. If adult tickets sold for $2.00 and children's tickets sold for $1.50, how many of each kind of ticket were sold?

Answer 1

ANSWER

475 adult tickets and 375 children tickets were sold

EXPLANATION

Let the number of adult tickets be a.

Let the number of children tickets be c.

The total number of tickets is 850. This means that:

$a+c=850$

The cost of all the tickets sold is $1512.50.

Each adult's ticket sold for $2.00 and each children ticket sold for $2.00.

Therefore, we have that:

$2a+1.5c=1512.50$

We now have a system of two simultaneous equations:

$\begin{gathered} a+c=850 \\ 2a+1.5c=1512.50 \end{gathered}$

From the first equation, make a subject of formula:

$a=850-c$

Substitute that into the second equation:

$\begin{gathered} 2(850-c)+1.5c=1512.50 \\ 1700-2c+1.5c=1512.50 \\ 1700-0.5c=1512.50 \\ \Rightarrow0.5c=1700-1512.50=187.50 \\ \Rightarrow c=\frac{187.50}{0.5} \\ c=375 \end{gathered}$

Recall that:

$a=850-c$

This means that:

$\begin{gathered} a=850-375 \\ a=475 \end{gathered}$

Therefore, 475 adult tickets and 375 children tickets were sold.