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. So we need to subtract the cost polynomial from the revenue polynomial.
Revenue: \( 3x^2 + 4x - 60 \)
Cost: \( 3x^2 - x + 200 \)

Step2: Subtract the Polynomials

\( (3x^2 + 4x - 60) - (3x^2 - x + 200) \)
Distribute the negative sign: \( 3x^2 + 4x - 60 - 3x^2 + x - 200 \)

Step3: 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 the profit expression is \( 5x - 260 \).

Answer:

C. \( 5x - 260 \) (assuming the third option is labeled C, if options are A, B, C, D with C being \( 5x - 260 \))