Question

the revenue, in dollars, of a company that makes toy cars can be modeled by the polynomial $3x^2 + 4x - 60$. the cost, in dollars, of producing the toy cars can be modeled by $3x^2 - x + 200$. the number of toy cars sold is represented by $x$. if the profit is the difference between the revenue and the cost, what expression represents the profit? $\bigcirc\\ 3x - 260$ $\bigcirc\\ 3x + 140$ $\bigcirc\\ 5x - 260$ $\bigcirc\\ 5x + 140$

Explanation:

Step1: Recall Profit Formula

Profit = Revenue - Cost. Given Revenue is \(3x^2 + 4x - 60\) and Cost is \(3x^2 - x + 200\).

Step2: Substitute into Formula

Profit = \((3x^2 + 4x - 60) - (3x^2 - x + 200)\)

Step3: Distribute the Negative Sign

Profit = \(3x^2 + 4x - 60 - 3x^2 + x - 200\)

Step4: Combine Like Terms

For \(x^2\) terms: \(3x^2 - 3x^2 = 0\)
For \(x\) terms: \(4x + x = 5x\)
For constant terms: \(-60 - 200 = -260\)
So Profit = \(5x - 260\)

Answer:

C. \(5x - 260\)