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2. A group of activists wants to raise money for a good cause, so they decide to sponsor a bicycle race. It receives $60 per cyclist entry and $15,000 in donations, but it must spend $18 per entry to cover the cost of the race.
Write and solve an inequality to determine the number of cyclists the group needs to raise at least $57,000. Be sure to define a variable and explain what your answer means in the context of the problem.

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Answer

Step-by-step explanation:

  • The number of cyclists the group needs to raise at least $57,000 must be at least 1000 cyclists
  • Let x represent the number of cyclists.
  • Since, the activists receive $60 per cyclist entry and $15,000 in donations, hence:
  • Revenue = 60x + 15000
  • Also, the cost of the race is $18 per entry, hence:
  • Cost = 18x
  • They need to raise at least $57,000, hence:
  • Profit ≥ 57000
  • Revenue - Cost ≥ 57000
  • (60x + 15000) - 18x ≥ 57000
  • 42x ≥ 42000
  • x ≥ 1000
  • Therefore the number of cyclists the group needs to raise at least $57,000 must be at least 1000 cyclists

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