Question

Tickets for a local high school student play are charged $4.00 for adults and $2.50 for students. If 410 tickets were sold for a total of $1505.00, how many adult tickets were sold?

Answer 1

To find the number of adult tickets sold, we can set up a system of equations using the information given. By solving these equations simultaneously, we can determine the value of x, which represents the number of adult tickets sold. The number of adult tickets sold is 320.

Step-by-step explanation:

To solve this problem, we can set up a system of equations. Let x represent the number of adult tickets sold and y represent the number of student tickets sold. We know that the cost of each adult ticket is $4.00 and the cost of each student ticket is $2.50. The total number of tickets sold is 410, so we have the equation x + y = 410. The total amount of money collected is $1505.00, so we have the equation 4x + 2.50y = 1505. We can solve these equations simultaneously to find the number of adult tickets sold.

Step 1: x + y = 410

Step 2: 4x + 2.50y = 1505

Step 3: Multiply the first equation by 2.50 to eliminate y: 2.50x + 2.50y = 1025

Step 4: Subtract the second equation from the third equation: 2.50x + 2.50y - (4x + 2.50y) = 1025 - 1505

Step 5: Simplify the equation: -1.5x = -480

Step 6: Divide both sides of the equation by -1.5: x = 320

Therefore, there were 320 adult tickets sold.