Question

For our class trip. 130 tickets were purchased. The cost of a faculty ticket was to

cost of a faculty ticket was $16,500. The
cost of a student ticket was $9.900. A total of $ 1,570.800 was collected. Algebraically.
determine how many faculty and how many student tickets were sold.

Answer 1

43 faculty tickets and 87 student tickets

Explanation:

Let x be the number of faculty tickets sold and y be the number of student tickets sold.

130 tickets were purchased, so

x + y = 130

The cost of faculty ticket was $16.50, then x tickets cost $16.50x.

The cost of student tickets sold was $9.90, then y tickets cost $9.90y.

A total of $ 1,570.80 was collected, thus

16.50x + 9.90y = 1,570.80

You get the system of two equations:

`\left\{\begin{array}{l}x+y=130\\ \\16.50x+9.90y=1,570.80\end{array}\right.`

From the first equation:

`x=130-y`

Substitute it into the second equation:

`16.5(130-y)+9.9y=1,570.8\\ \\165(130-y)+99y=15,708\\ \\55(130-y)+33y=5,236\\ \\7,150-55y+33y=5,236\\ \\-55y+33y=5,236-7,150\\ \\-22y=-1,914\\ \\22y=1,914\\ \\y=87\\ \\x=130-87=43`

43 faculty tickets and 87 student tickets