Question

1775 concert tickets were sold for a total of $4022. If students paid $2 and non-students paid $3, how many tickets were sold to each group?

a) 1225 tickets were sold to students.
b) 550 tickets were sold to non-students.
c) Both a and b
d) None of the above

Answer 1

1225 tickets were sold to students and 550 tickets were sold to non-students.

Step-by-step explanation:

To solve this problem, we can set up a system of equations. Let's let x represent the number of student tickets sold and y represent the number of non-student tickets sold. The total number of tickets sold is 1775, so we have the equation x + y = 1775. The total amount of money collected is $4022, so we have the equation 2x + 3y = 4022. Now we can solve these equations simultaneously.

Multiplying the first equation by 2, we get 2x + 2y = 3550. Subtracting this equation from the second equation, we get y = 472. Substituting this value back into the first equation, we get x + 472 = 1775, so x = 1303. Therefore, 1225 tickets were sold to students (choice a) and 550 tickets were sold to non-students (choice b).