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AlgebraEasyReading a linear function's parts

Algebra practice question

A plumber charges a call-out fee of $40 plus $3 for each minute of work. Which function gives the total charge C(m), in dollars, for a job lasting m minutes?

  1. A. C(m) = 3m + 40Correct
  2. B. C(m) = 40m + 3
  3. C. C(m) = 43m
  4. D. C(m) = 3(m + 40)

Answer: A. C(m) = 3m + 40

The $40 is paid once (the constant); the $3 is paid for each of the m minutes (3m). Total: 3m + 40. Check: 12 minutes cost 36 + 40 = $76.

Why the other answers are wrong

B. C(m) = 40m + 3
40m + 3 charges $40 per minute and $3 once — the two amounts are swapped.
C. C(m) = 43m
43m charges $43 every minute; the $40 is a one-time fee, not a per-minute rate.
D. C(m) = 3(m + 40)
3(m + 40) = 3m + 120, which charges $120 up front instead of $40.

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