Answer:
- adult: $13.75
- child: $10.25
Step-by-step explanation:
You have two revenue relations and want the price of each adult and child ticket. 150 adult and 100 child tickets sold for $3087.50; 200 adult and 150 child tickets sold for $4287.50.
Equations
Each of the revenue relations can be formulated as an equation. If x and y represent the price of each adult and child ticket, respectively, then ...
150x +100y = 3087.50
200x +150y = 4287.50
Solution
The solution can be found many ways. A graphing calculator (first attachment) shows the solution to be ...
- adult price: $13.75
- child price: $10.25
The calculator function that reduces a matrix to row-echelon form can be used on the augmented matrix of coefficients. That, too, gives the solution about as quickly as you can enter the coefficients. This is shown in the second attachment.
Subtracting twice the second equation from 3 times the first will eliminate the y-variable:
3(150x +100y) -2(200x +150y) = 3(3087.50) -2(4287.50)
50x = 687.50
x = 13.75 . . . . . . divide by 50
From the second equation, ...
y = (4287.50 -200(13.75))/150 = 1537.50/150
y = 10.25
