SAT Math Multiple Choice Question 606: Answer and Explanation
6. The cost in dollars, C, to manufacture n necklaces is given by the equation C(n) = an + b, where a and b are positive constants. In this equation, what does a represent?
- A. the fixed costs, in dollars, independent of any necklaces being manufactured
- B. the total cost, in dollars, to produce n necklaces, not including fixed costs
- C. the total cost, in dollars, to produce one necklace, including fixed costs
- D. the cost, in dollars, to produce one necklace, not including any fixed costs
Correct Answer: D
Algebra (linear equations) MEDIUM
C(n) = an + b
Since this expression is linear in n (the input variable, which represents the number of necklaces produced), the constant a represents the slope of this line, which in turn represents the "unit rate of increase," in other words, the increase in total cost for each individual necklace produced.
The constant b represents the "y-intercept" of this line, which in this case means the costs when n = 0 (that is, the fixed costs before any necklaces are produced).