hi can someone help me with this problem. i cant figure out which equation to use. thanks
a full-price ticket for a college basketball game costs $2.50, and a student ticket costs $1.75. if 585 tickets were sold , and the total reciepts were $1,217,25, how many tickets were student tickets?
Let x = number of full price tickets and y = number of student tickets.
x + y = 585, then x = 585 - y
2.5x + 1.75y = 1217.25
Substitute 585 - y for x in second equation and solve for y.
I hope this helps. Thanks for asking.
To solve this problem, we need to set up a system of equations. Let's define two variables:
Let x represent the number of full-price tickets sold.
Let y represent the number of student tickets sold.
We know that a full-price ticket costs $2.50. Therefore, the total revenue from full-price tickets is 2.50x dollars.
Similarly, we know that a student ticket costs $1.75. Therefore, the total revenue from student tickets is 1.75y dollars.
We are given two pieces of information:
1) The total number of tickets sold is 585 tickets:
x + y = 585
2) The total revenue from all tickets sold is $1,217.25:
2.50x + 1.75y = 1217.25
Now we have a system of two equations:
x + y = 585 (Equation 1)
2.50x + 1.75y = 1217.25 (Equation 2)
To find the number of student tickets, we need to solve this system of equations.
One way to solve it is by substitution. Let's solve Equation 1 for x:
x + y = 585
x = 585 - y
Now substitute this expression for x into Equation 2:
2.50(585 - y) + 1.75y = 1217.25
Simplify and solve for y:
1462.5 - 2.50y + 1.75y = 1217.25
-0.75y = 1217.25 - 1462.5
-0.75y = -245.25
y = (-245.25) / (-0.75)
y ≈ 327
Therefore, the number of student tickets sold is approximately 327.