College Algebra Help!

Question

The school production of​ 'Our Town' was a big success. For opening​ night,

511 tickets were sold. Students paid

​$4.00

​each, while​ non-students paid

​$6.00

each. If a total of

$ 2408.00

was​ collected, how many students and how many​ non-students attended?

The number of students was

______.

​(Simplify your​ answer.)

The number of​ non-students was

_______.

​(Simplify your​ answer.)

Answer 1

Let's use the variable s to represent the NUMBER of student tickets and the variable x represent the NUMBER of non-student tickets. Since there are a total of 511 tickets , we can write:

s + x = 511

Then since it costs $4 for each student ticket and $6 for each non-student ticket, we can represent the total money spent by:

4s + 6x = $2408

To solve these two equations with two unknowns, use substitution.

From the first equation we can write that s = 511 - x

Substitute this expression for s into the second equation:

4s + 6x = $2408

4 (511 - x) + 6x = 2408

2044 - 4x + 6x = 2408

2044 + 2x = 2408

2044 + 2x - 2044= 2408 - 2044

2x = 364

x = 182

Therefore, 182 non-student tickets were sold.

The number of student tickets will be 511 - 182 or 329 student tickets.

To verify: 4 * 329 + 6 * 182 = 1316 + 1092 = 2408