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.
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
Thank you.
To write the equation that explains the profit made last year, we need to use the given information.
The revenue from ticket sales is given as 4x(x+6), where 'x' represents some variable.
The cost of the band is given as 5x(x-4).
The profit is given as $160,000.
The equation to determine profit is Revenue – Cost = Profit. Therefore, we can write the equation as:
4x(x+6) - 5x(x-4) = 160
Now let's simplify this equation by expanding and combining like terms:
4x^2 + 24x - 5x^2 + 20x = 160
Next, let's combine the like terms on the left-hand side of the equation:
(4x^2 - 5x^2) + (24x + 20x) = 160
Simplifying further, we have:
-x^2 + 44x = 160
This is the equation that explains the profit made last year.