Set up a system of equations display it and then use it to s

Set up a system of equations, display it, and then use it to solve this problem: two thousand tickets were sold, which generated $19,700. The prices of the tickets were $5 for children, $10 for students, and $12 for adults. There were 100 more adult tickets sold than student tickets.

Solution

Let x be the no. of child tickets

Let y be no. of student tickets

Let z be the no. of adult tickets

x+y+z = 2000 -----(1)

The prices of the tickets were $5 for children, $10 for students, and $12 for adults.

5x +10y +12z = 19700 -----(2)

There were 100 more adult tickets sold than student tickets.

z = 100+ y ----(3)

-y +z =100

We have three equations with three varaible solve to find x, y, z.

Multiply first equation by 5 and add the result to the second equation. The result is:

x+y+z = 2000

5y +7z = 9700

-y +z =100

Swap Row 2 and Row 3.After this step we have:

x+y+z = 2000

5y +7z = 9700

12z = 10200

z= 850 tickets for adult

y = 750 tickets for students

x = 2000 -850 -750 = 400 for children