The juniors sold the student tickets for $3 and he adult tickets for $8 use a to represent the number of tickets that were sold. In total 300 tickets were sold. After paying back the investors, the profit was $775. If the juniors initially received a total of $210 from investors , how many tickets of each type did the students sell?

283 student tickets and 17 adult tickets were sold.

Step-by-step explanation:

Let x represent the number of student tickets that they sold.

Let y represent the number of adult tickets that they sold.

In total 300 tickets were sold. It means that

x + y = 300

The juniors sold the student tickets for $3 and he adult tickets for $8. After paying back the investors, the profit was $775. If the juniors initially received a total of $210 from investors, it means that the total revenue from the ticket sales is

775 + 210 = 985

The expression becomes

3x + 8y = 985- - - - - - - - - - -1

Substituting x = 300 - y into equation 1, it becomes

3(300 - y) + 8y = 985

900 - 3y + 8y = 985

- 3y + 8y = 985 - 900

5y = 85

y = 85/5

y = 17

x = 300 - y = 300 - 17

x = 283

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