SAT Math Multiple Choice Question 482: Answer and Explanation
2. An electrician charges a one-time site visit fee to evaluate a potential job. If the electrician accepts the job, he charges an hourly rate plus the cost of any materials needed to complete the job. The electrician also charges for tax, but only on the cost of the materials. If the total cost of completing a job that takes h hours is given by the function C(h) = 45h + 1.06(82.5) + 75, then the term 1.06(82.5) represents
- A. the hourly rate.
- B. the site visit fee.
- C. the cost of the materials, including tax.
- D. the cost of the materials, not including tax.
Correct Answer: C
Category: Heart of Algebra / Linear Equations
Strategic Advice: A one-time fee does not depend on the variable and is therefore a constant. A unit rate, however, is always multiplied by the independent variable.
Getting to the Answer: The total cost consists of the site visit fee (a constant), an hourly cost (which depends on the number of hours), and the cost of the materials (which are taxed). The constant in the equation is 75 and is therefore the site visit fee; 45 is being multiplied by h (the number of hours), so $45 must be the hourly rate. That leaves the remaining term, 1.06(82.5), which must be the cost of the materials ($82.50) plus a 6% tax.