Answered

Westonci.ca is your trusted source for finding answers to all your questions. Ask, explore, and learn with our expert community. Experience the ease of finding accurate answers to your questions from a knowledgeable community of professionals. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

The revenue, in dollars, of a company that produces jeans is modeled by [tex]\(2x^2 + 17x - 175\)[/tex]. The cost, in dollars, of producing the jeans is modeled by [tex]\(2x^2 - 3x - 125\)[/tex]. The number of pairs of jeans sold is represented by [tex]\(x\)[/tex].

If profit is the difference between revenue and cost, which expression can be used to find profit, and what is that profit when 75 pairs of jeans are sold?

A. [tex]\(20x - 50\)[/tex]; \[tex]$500
B. \(20x - 50\); \$[/tex]1,450
C. [tex]\(20x + 50\)[/tex]; \[tex]$1,550
D. \(20x + 50\); \$[/tex]5,250

Sagot :

GinnyAnswer
To determine the correct expression for the profit and the profit value when 75 pairs of jeans are sold, follow these steps:

### Step-by-Step Solution

1. Identify the expressions for revenue and cost:

The revenue function is given by:
[tex]\[ \text{Revenue} = 2x^2 + 17x - 175 \][/tex]

The cost function is given by:
[tex]\[ \text{Cost} = 2x^2 - 3x - 125 \][/tex]

2. Formulate the profit function:

Profit is calculated as the difference between revenue and cost.

[tex]\[ \text{Profit} = \text{Revenue} - \text{Cost} \][/tex]

Substitute the given expressions:

[tex]\[ \text{Profit} = (2x^2 + 17x - 175) - (2x^2 - 3x - 125) \][/tex]

3. Simplify the profit expression:

Combine like terms:

[tex]\[ \text{Profit} = 2x^2 + 17x - 175 - 2x^2 + 3x + 125 \][/tex]

Simplify further by combining [tex]\(2x^2\)[/tex] terms which cancel each other out:

[tex]\[ \text{Profit} = 17x + 3x - 175 + 125 \][/tex]

[tex]\[ \text{Profit} = 20x - 50 \][/tex]

Therefore, the expression for profit is:

[tex]\[ \text{Profit} = 20x - 50 \][/tex]

4. Calculate the profit when [tex]\( x = 75 \)[/tex]:

Substitute [tex]\( x = 75 \)[/tex] into the profit expression:

[tex]\[ \text{Profit} = 20(75) - 50 \][/tex]

Calculate the value:

[tex]\[ \text{Profit} = 1500 - 50 \][/tex]

[tex]\[ \text{Profit} = 1450 \][/tex]

### Conclusion:

The correct expression for the profit is [tex]\(20x + 50\)[/tex] (not [tex]\(20x - 50\)[/tex]) and the profit when 75 pairs of jeans are sold is \[tex]$1,450. Therefore, the correct answer is: \[ \boxed{20x + 50 ; \$[/tex] 1,450}
\]
We appreciate your time. Please revisit us for more reliable answers to any questions you may have. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.