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A coffee shop is analyzing its resource usage to improve efficiency. The shop finds that the amount of coffee beans needed increases with the number of cups of coffee made. The brewing time for a batch of 100100 cups of coffee is reduced as more brewing machines are used. If one machine takes 3030 minutes to brew the batch, the time decreases with the use of additional machines.A coffee shop is analyzing its resource usage to improve efficiency. The shop finds that the amount of coffee beans needed increases with the number of cups of coffee made. The brewing time for a batch of 100100 cups of coffee is reduced as more brewing machines are used. If one machine takes 3030 minutes to brew the batch, the time decreases with the use of additional machines.

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Q. A coffee shop is analyzing its resource usage to improve efficiency. The shop finds that the amount of coffee beans needed increases with the number of cups of coffee made. The brewing time for a batch of 100100 cups of coffee is reduced as more brewing machines are used. If one machine takes 3030 minutes to brew the batch, the time decreases with the use of additional machines.\newline(a) If 33 brewing machines are used, how long will it take to brew 100100 cups of coffee, assuming the same batch size and efficiency?\newline(b) How many brewing machines are required to brew 100100 cups of coffee in 1515 minutes?
  1. Calculate time with 33 machines: (a) Calculate the time with 33 machines. Time with 11 machine = 3030 minutes. Time with 33 machines = 303=10\frac{30}{3} = 10 minutes.
  2. Calculate machines for 1515 minutes: (b) Calculate the number of machines needed for 1515 minutes. Time with 11 machine == 3030 minutes. Machines needed == 3015\frac{30}{15} == 22 machines.

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