In the community you live, you have been asked to serve on the planning committee for the Fourth of July festival. Your committee has decided to begin meeting early to avoid some of the problems experienced in previous years. Unfortunately, those problems stemmed from poor budgeting and record keeping. To ensure that the festival at least breaks even and does not cost more than it brings into the town, you are reviewing information kept from the previous year. You are particularly interested in the big name band brought in, and determining how to make the most profit from ticket sales this coming year. The following information is given:

Question

In the community you live, you have been asked to serve on the planning committee for the Fourth of July festival.  Your committee has decided to begin meeting early to avoid some of the problems experienced in previous years.  Unfortunately, those problems stemmed from poor budgeting and record keeping.  To ensure that the festival at least breaks even and does not cost more than it brings into the town, you are reviewing information kept from the previous year.  You are particularly interested in the big name band brought in, and determining how to make the most profit from ticket sales this coming year.  The following information is given:

Revenue from ticket sales: 4x(x+6)
Cost of band: 5x((x-4)
Profit:  160 (given in thousands)

The equation to determine profit is Revenue – Cost = Profit.  Write the equation that explains the profit made last year.  Be certain to combine like terms.

Dr Russ · Answer

Revenue – Cost = Profit substitute the terms [4x(x+6)] - [5x(x-4)] = 160,000 expand 4x^2 + 24x - 5x^2 + 20x = 160,000 combine like terms -x^2 + 44x - 160,000 = 0

Kelly · Answer

Thank you.