Question bank / Linear functions

Math · AlgebraMedium

A party rental company charges $85\$85 to rent a bounce house for the first 33 hours and $20\$20 for each additional hour. Which function gives the total cost C(h)C(h), in dollars, to rent the bounce house for hh hours, where h≥3h \ge 3?

A

C(h)=20h+25C(h) = 20h + 25

B

C(h)=20h+85C(h) = 20h + 85

C

C(h)=20h+145C(h) = 20h + 145

D

C(h)=85h+20C(h) = 85h + 20

Show answer and explanation

Answer: A

The first 33 hours cost $85\$85, and each of the remaining h−3h - 3 hours costs $20\$20. So C(h)=85+20(h−3)=85+20h−60=20h+25C(h) = 85 + 20(h - 3) = 85 + 20h - 60 = 20h + 25. Check: C(3)=60+25=85C(3) = 60 + 25 = 85.

Choice B charges $20\$20 for every hour, including the first 33 hours that the $85\$85 already covers.

Why the other choices are wrong

  • B. This charges $20 for all h hours, including the first 3, which the $85 already covers. It gives C(3) = 145.
  • C. This uses 85 + 20(h + 3), which adds 3 hours instead of subtracting them.
  • D. This switches the roles of the numbers, charging $85 per hour plus a one-time $20.
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