Full-price tickets for a concert cost \( \$ 56.50 \). Students can purchase a discounted ticket for \( \$ 47.50 \). If a total of 3250 tickets are sold and if the total amount of ticket sales was \( \$ 156,571 \), a) how many full-price tickets were sold? b) how many student tickets were sold? a) The number of full-price tickets sold is (Type an integer or a decimal.)

To solve this problem, let \( x \) be the number of full-price tickets sold, and \( y \) be the number of student tickets sold. We have two equations based on the information provided: 1. \( x + y = 3250 \) (the total number of tickets sold) 2. \( 56.50x + 47.50y = 156,571 \) (the total sales amount) Now, we can solve these equations. From the first equation, we can express \( y \) in terms of \( x \): \[ y = 3250 - x \] Substituting this into the second equation: \[ 56.50x + 47.50(3250 - x) = 156,571 \] Distributing the \( 47.50 \): \[ 56.50x + 154375 - 47.50x = 156,571 \] Combining like terms: \[ (56.50 - 47.50)x + 154375 = 156,571 \] \[ 9x + 154375 = 156,571 \] Subtracting \( 154375 \) from both sides: \[ 9x = 2,196 \] Now, divide by 9: \[ x = \frac{2196}{9} \] \[ x = 244 \] So, the number of full-price tickets sold is \( \boxed{244} \). To find out how many student tickets were sold, substitute \( x \) back into the first equation: \[ y = 3250 - 244 = 3006 \] Thus, the number of student tickets sold is \( \boxed{3006} \).