Question

The theater performed a show last Saturday. Student tickets cost $5 each, and adult tickets cost $7 each. In all, 290 people attended the show, and $1,790 was the total for all ticket sales. How many student and adult tickets were sold?

a) x student tickets and y adult tickets were sold, where x = 120 and y = 170.
b) x student tickets and y adult tickets were sold, where x = 170 and y = 120.
c) x student tickets and y adult tickets were sold, where x = 100 and y = 190.
d) x student tickets and y adult tickets were sold, where x = 190 and y = 100.

Answer 1

To solve this problem, set up a system of equations with x and y representing the number of student and adult tickets sold. None of the options provided are correct.

Step-by-step explanation:

To solve this problem, we can set up a system of equations. Let x be the number of student tickets sold and y be the number of adult tickets sold.

We know that the cost of a student ticket is $5 and the cost of an adult ticket is $7.

From the given information, we can write the following equations:

x + y = 290 (equation 1)

5x + 7y = 1790 (equation 2)

We can solve this system of equations to find the values of x and y:

Multiplying equation 1 by 5, we get:

5x + 5y = 1450 (equation 3)

Subtracting equation 3 from equation 2, we get:

5y - 5y = 1790 - 1450

0 = 340

This is not possible, so there is no solution that satisfies both equations. Therefore, none of the given options (a, b, c, or d) is correct.