number of student tickets sold (x) = 40
number of adult tickets sold (y) = 60
Step-by-step explanation:
Let x = number of student tickets sold
Let y = number of adult tickets sold
Given:
total ticket sales = 100⇒ x + y = 100
Given:
student ticket = $4adult ticket = $8total ticket sales = $640⇒ 4x + 8y = 640
Rewrite x + y = 100 to make x the subject:
⇒ x = 100 - y
Substitute x = 100 - y into 4x + 8y = 640 and solve for y:
⇒ 4(100 - y) + 8y = 640
⇒ 400 - 4y + 8y = 640
⇒ 4y = 240
⇒ y = 60
Substitute found value for y into x = 100 - y and solve for x:
⇒ x = 100 - 60
⇒ x = 40
To solve graphically, rewrite both equations to make y the subject:
y = 100 - x
y = 80 - (1/2)x
Plot both lines.
The solution is the point of intersection (40, 60)