A theater holds 2,680 seats. The lower level has 100 less than 2 times as many seats as the upper level. The middle level has 80 more than 3 times as many seats as the upper level. How many seats are in the middle level?

Assign variables to make things easier:

a = Upper

b = Middle

c = Lower

Equations:

c = 2a-100

b = 3a+80

a = a

(2a-100) + (3a+80) + (a) = 2680

6a-20 = 2680

6a = 2700

a = 450

Now plug a into the middle equation:

b = 3a+80

b = 3 (450) + 80

b = 1350+80

b = 1430

The middle level has 1430 seats.

You can check this by solving for the upper level and checking all 3 levels equal 2680.

c = 2a-100

(skipping steps)

c=800

Totals:

a = Upper = 450

b = Middle = 1430

c = Lower = 800

Total: 2680