AlgebraHardModel from two data points
Algebra practice question
A window cleaner charges a fixed fee plus a rate per window. Cleaning 2 windows costs $38 and cleaning 6 windows costs $74. Which function gives the cost C, in dollars, of cleaning w windows?
- A. C(w) = 9w + 20Correct
- B. C(w) = 19w
- C. C(w) = 9w + 38
- D. C(w) = 12w + 14
Answer: A. C(w) = 9w + 20
Rate: (74 − 38)/(6 − 2) = $9 per window. Fee: 38 − 9 × 2 = $20.
Why the other answers are wrong
- B. C(w) = 19w
- 19w fits 2 windows but gives 114 for 6.
- C. C(w) = 9w + 38
- 9w + 38 uses the 2-window cost as the fee; check w = 2: 56 ≠ 38.
- D. C(w) = 12w + 14
- 12w + 14 gives 38 at w = 2 but 86 at w = 6.
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