Question

The talent show committee sold a total of 875 tickets in advance. Student tickets cost $4.50 each and the adult tickets cost $10 each. If the total receipts were $6825, how many of each type of ticket were sold? The following system of equations can be used to represent the situation.

begin mathsize 12px style open curly brackets table attributes columnalign left end attributes row cell a plus c equals 875 end cell row cell 10 a plus 4.5 c equals 6825 end cell end table close end style

Define each variable.

Answer 1

525 adult and 350 student tickets were sold

Explanation:

Let
`s` be the number of student tickets and
`a` be the number of adult tickets:

`4.50s+10a=6825\\s+a=875\\\\s=875-a\\\\4.50(875-a)+10a=6825\\3937.5-4.5a+10a=6825\\5.5a=2887.5\\a=525\\\\s=875-525=350`

Therefore, there were 525 adult tickets and 350 student tickets sold.