Questions: Suppose the cost of manufacturing 70 widgets is 5,130, and the cost of manufacturing 125 widgets is 6,725. - Which statement below best describes the situation? The number of widgets made depends on the cost of making them. - The cost of making widgets depends on the number of widgets made. Use this information and what you learned in the previous examples to determine if the cost of the widgets or the number of widgets made is represented by x. What does y represent? How do you decide? Let x= number of widgets cost of making them - How much does each additional widget add to the total manufacturing cost?

Suppose the cost of manufacturing 70 widgets is 5,130, and the cost of manufacturing 125 widgets is 6,725. - Which statement below best describes the situation? The number of widgets made depends on the cost of making them. - The cost of making widgets depends on the number of widgets made. Use this information and what you learned in the previous examples to determine if the cost of the widgets or the number of widgets made is represented by x. What does y represent? How do you decide? Let x= number of widgets cost of making them - How much does each additional widget add to the total manufacturing cost?
Transcript text: - Suppose the cost of manufacturing 70 widgets is $\$ 5,130$, and the cost of manufacturing 125 widgets is $\$ 6,725$. - Which statement below best describes the situation? The number of widgets made depends on the cost of making them. - The cost of making widgets depends on the number of widgets made. Use this information and what you learned in the previous examples to determine if the cost of the widgets or the number of widgets made is represented by $x$. What does $y$ represent? How do you decide? Let $x=$ number of widgets $\qquad$ cost of making them - How much does each additional widget add to the total manufacturing cost?
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Solution

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Solution Steps

Step 1: Identify the given information
  • Cost of manufacturing 70 widgets: $5,130
  • Cost of manufacturing 125 widgets: $6,725
Step 2: Define variables
  • Let \( x \) = number of widgets
  • Let \( y \) = cost of making them
Step 3: Determine the cost per additional widget
  • Calculate the difference in cost: \( 6,725 - 5,130 = 1,595 \)
  • Calculate the difference in the number of widgets: \( 125 - 70 = 55 \)
  • Cost per additional widget: \( \frac{1,595}{55} = 29 \)

Final Answer

Each additional widget adds $29 to the total manufacturing cost.

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