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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



Answer :

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: \[ \boxed{20x + 50 ; \$[/tex] 1,450}
\]

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