Final answer:
Upon solving the system of equations, it was found that 342 student tickets and 408 non-student tickets were sold. This answer is not listed among the provided options, indicating a possible error in the question or answer choices.Students: 250, Non-students: 500
Step-by-step explanation:
The question asks us to determine the number of student tickets and non-student tickets sold for a community college spring musical, given that student tickets cost $3 each, non-student tickets cost $5 each, a total of 750 tickets were sold, and the total receipts were $3066.Let's denote the number of student tickets as s and the number of non-student tickets as n. We have two equations from the information given: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 non-student tickets sold. We are given two pieces of information:The total number of tickets sold is 750: x + y = 750The total receipts were $3066: 3x + 5y = 3066We can solve this system of equations using substitution or elimination. Here, we will use substitution.From the first equation, we can solve for x in terms of y: x = 750 - y.Substituting this into the second equation:3(750 - y) + 5y = 30662250 - 3y + 5y = 30662y = 816y = 408Now, we can substitute this value of y back into the first equation to find x:x + 408 = 750x = 342Therefore, the number of student tickets sold is 342 and the number of non-student tickets sold is 408.s + n = 750 (total tickets3s + 5n = 3066 (total receipts)To solve this system of equations, we can use the substitution or elimination method.
For simplicity, let's use the elimination method:Multiply the first equation by 3 to get: 3s + 3n = 2250Now subtract this new equation from the second equation provided by the problem: (3s + 5n = 3066) - (3s + 3n = 2250), which simplifies to 2n = 816.Dividing both sides of the equation by 2, we find n = 408 non-student tickets.To find s, plug the value of n back into the first equation: s + 408 = 750, which simplifies to s = 342 student ticketsTo 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 non-student tickets sold. We are given two pieces of information:The total number of tickets sold is 750: x + y = 750The total receipts were $3066: 3x + 5y = 3066We can solve this system of equations using substitution or elimination. Here, we will use substitution.From the first equation, we can solve for x in terms of y: x = 750 - y.Substituting this into the second equation:3(750 - y) + 5y = 3066- 3y + 5y = 30662y = 816y = 408Now, we can substitute this value of y back into the first equation to find x:x + 408 = 750x = 342Therefore, the number of student tickets sold is 342 and the number of non-student tickets sold is 40Therefore, the correct answer is not explicitly listed in the options, which means there might be an error in the question or the provided choices.