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

475 adult tickets and 375 children tickets were sold

Step-by-step 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=(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.