Question

the revenue, in dollars, of a company that produces jeans can be modeled by $2x^2 + 17x - 175$. the cost, in dollars, of producing the jeans can be modeled by $2x^2 - 3x - 125$. the number of pairs of jeans that have been sold is represented by $x$. if the profit is the difference between the revenue and the cost, which expression can be used to find profit and what is that profit when 75 pairs of jeans are sold?

• $20x - 50$; $\\$500$
• $20x - 50$; $\\$1,450$
• $20x + 50$; $\\$1,550$
• $20x + 50$; $\\$5,250$

Explanation:

Step1: Find the profit expression

Profit = Revenue - Cost. Given Revenue = \(2x^2 + 17x - 175\) and Cost = \(2x^2 - 3x - 125\). Subtract Cost from Revenue:
\[

$$\begin{align*} (2x^2 + 17x - 175) - (2x^2 - 3x - 125) &= 2x^2 + 17x - 175 - 2x^2 + 3x + 125\\ &= (2x^2 - 2x^2) + (17x + 3x) + (-175 + 125)\\ &= 20x - 50 \end{align*}$$

\]

Step2: Calculate profit when \(x = 75\)

Substitute \(x = 75\) into the profit expression \(20x - 50\):
\[
20(75) - 50 = 1500 - 50 = 1450
\]

Answer:

B. \(20x - 50\); \(\$1,450\)