Question

For a school drama performance, student tickets cost $5 each and adult tickets cost $10 each. The sellers collected $3,570 from 512 tickets sold. If c is the number of student tickets sold, which equation can be used to find the amount of tickets sold of each type?

Answer 1

5c+10a=3570 c+a=512 ... a=512-c so ... 5c + 10(512-c)=3570

Answer 2

The system of equations is equal to

`a+c=512`

`5c+10a=3,570`

The number of adult tickets sold is
`a=202\ tickets`

The number of student tickets sold is
`c=310\ tickets`

Explanation:

Let

c------> the number of student tickets sold

a-----> the number of adult tickets sold

we know that

`a+c=512` -----> equation A

`5c+10a=3,570` -----> equation B

Using a graphing tool

The solution of the system of equations is the intersection point both graphs

see the attached figure

The intersection point is
`(202,310)`

therefore

the solution is

the number of adult tickets sold is
`a=202\ tickets`

the number of student tickets sold is
`c=310\ tickets`