This time, we are given that there were 3 times as many student tickets sold as adult tickets. Also, we know that 480 tickets were sold in total. We want to calculate the ticket sales and how much below the goal of $2050 they fell. To do that, we will first find the number of adult tickets sold d and the number of student tickets sold s.
d& ← Number of adult tickets sold
s& ← Number of student tickets sold
Let's try to form a system of equations for d and s. We know that there were 3 times as many student ticket sold s as adult tickets d.
s= 3* d
Also, we know that 480 tickets were sold in total. This means that the sum of student and adult tickets must be equal to 480.
s+d= 480
We created two equations for s and d! Together they form a system of equations.
s=3d & (I) s+d=480 & (II)
We can solve this system using substitution. Notice that the first equations is solved for s. Thus, we can substitute s= 3d into the second equation.
s=3d s+d=480
s=3d 3d+d=480
s=3d 4d=480
s=3d d=480/4
s=3d d=120
We found that d=120. Now, to find s we can substitute d=120 into the first equation.
s=3d d=120
s=3( 120) d=120
s=360 d=120
We found the number of adult tickets sold, d= 120, and the number of student tickets sold, s=360. Now, to find the sales we need to multiply the numbers of adult and student tickets by their corresponding ticket prices. Adult tickets cost $6.50 each, and student tickets cost $3.50 each.
Sales= 120* 6.50+360* 3.50
⇕
Sales=780+1260=2 040
We found that the sales are $2040, which is $10 under the goal of $2050.
