SAT Math Practice: Understanding Linear Cost Functions

Looking for free SAT practice questions that test your understanding of linear functions? This step-by-step solution explores how to interpret the components of a cost function—a common concept tested on the SAT Math section. Mastering these interpretations is crucial for success on your SAT test.

Question

The function C(x) = 15x + 200 represents the total cost in dollars to manufacture x skateboards. What is the meaning of the number 15 in this context?

  1. The cost to manufacture an additional skateboard
  2. The fixed overhead cost
  3. The number of skateboards produced
  4. The profit per skateboard

Step-by-Step SAT Math Solution

To solve this free SAT practice question, we'll analyze the function systematically:

  1. Identify what we're given:
    • C(x) = 15x + 200 represents the total cost in dollars
    • x represents the number of skateboards manufactured
    • We need to interpret what 15 means in this context
  2. Analyze how the function behaves with different values:
    • When x = 0: C(0) = 15(0) + 200 = $200
    • When x = 1: C(1) = 15(1) + 200 = $215
    • When x = 2: C(2) = 15(2) + 200 = $230
    • When x = 3: C(3) = 15(3) + 200 = $245
  3. Observe the pattern:
    • Each additional skateboard increases the total cost by $15
    • This means $15 is the additional cost for each skateboard manufactured
  4. Interpret the components of the linear function C(x) = 15x + 200:
    • 15 is the slope of the function, representing the rate of change
    • In this context, 15 represents the marginal cost or the cost to manufacture each additional skateboard
    • 200 is the y-intercept, representing the fixed costs that don't change regardless of production volume
  5. Eliminate incorrect options:
    • B) Fixed overhead cost would be 200, not 15
    • C) x represents the number of skateboards, not 15
    • D) The function only describes costs, not profit

A) - The cost to manufacture an additional skateboard is the answer

Key Takeaways for SAT Test Prep

This free SAT practice question highlights important concepts frequently tested on the SAT:

  • Interpreting components of linear functions in real-world contexts
  • Understanding the meaning of slope as a rate of change
  • Distinguishing between variable costs and fixed costs

This particular SAT practice problem also incorporates real-world applications of math, which is another common theme in SAT questions. Being able to translate word problems into mathematical equations is a crucial skill for SAT success.

For more free SAT practice materials and additional SAT practice questions with detailed explanations like this one, bookmark our SAT Question Bank and SAT study help blog.

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