Question

Regent Stadium charges $20 for a seat in the bleachers, $30 for an end zone seat, and $40 for the excellent seats near the 50-yard line. When the stadium is full, 500 tickets were sold for a total of $14,000. The number of bleacher seats is the same as the number of end zone and 50-yard line seats combined.

Answer 1

The number of bleachers seat sold = 200

The number of end zone seats sold =200

The number of excellent seats sold =100

Explanation:

Let there are bleachers seats =x

The number of zone seats =y

The number of excellent seats =z

So, we can set up equations for given sentences as

x+y+z= 500

20 x+30 y+40 z=14000

x=y

Substitute x as y into first two equations

y+y+z=500

20 y+30 y+40 z=14000

Simplify each

2 y+z=500

50 y+40 z= 14000

Multiply 2 y +z=500 by -40 to eliminate z terms when we add them.

-80 y-40 z=-20000

Add this with 50 y +40 z=14000, which gives

-30 y=-6000

Divide both sides by -30

y=200

Now, plug in y as 200 into any of the equations to find z.

2(200)+z=500

400+z =500

Subtract both sides 400.

z=100

Now, we know x=y

So, x=200