Question

A local theater company is presenting a musical for kids at the community center. Each adult ticket costs $8, and each child ticket

costs $4. On the opening night, the theater company needs to earn at least $1,280 from ticket sales to cover its costs. The communi
center has a capacity of 240 people.
If the solution region represents the number of adult and child tickets that needs to be sold for the theater company to cover its cost
determine which graph represents the solution set to the system of inequalities representing this situation.

Answer 1

Option (1)

Explanation:

Let the number of adult tickets sold = x

And the number of child tickets sold = y

Cost of adult tickets sold = $8x

And the cost of child tickets sold = $4y

If the theater company needs to earn at least $1280,

8x + 4y ≥ 1280

2x + y ≥ 320 ---------(1)

Since community center has a capacity of 240 people,

x + y ≤ 240 ----------(2)

By graphing these inequalities with the help of a graphing tool,

Shaded area above the solid line will be represented by inequality (1) (red line)

And the shaded area below the line will be the represented by inequality (2) (blue line)

Common area of both the shaded regions will represent the solution area .

Option (1) will be the answer.