Anouk is an engineer planning sound and lighting for a free concert in the park. The concert was advertised with a promise to use no more than 108 kilowatts (kW) of power. It was determined that the main contributors to power usage, speakers and floodlights, use 1.8kW and 2.2kW, respectively. Anouk also must keep within her budget of $3,300. The rental company is charging $75 for each speaker and $42 for each floodlight. Which of the following combinations meets Anouk's requirements?Choose 1 answer:(A) 40 speakers and 30 floodlights(B) 12 speakers and 54 floodlights(C) 26 speakers and 13 floodlights(D) 38 speakers and 22 floodlights
Q. Anouk is an engineer planning sound and lighting for a free concert in the park. The concert was advertised with a promise to use no more than 108 kilowatts (kW) of power. It was determined that the main contributors to power usage, speakers and floodlights, use 1.8kW and 2.2kW, respectively. Anouk also must keep within her budget of $3,300. The rental company is charging $75 for each speaker and $42 for each floodlight. Which of the following combinations meets Anouk's requirements?Choose 1 answer:(A) 40 speakers and 30 floodlights(B) 12 speakers and 54 floodlights(C) 26 speakers and 13 floodlights(D) 38 speakers and 22 floodlights
Calculate Power Usage: First, let's calculate the total power usage for each combination to ensure it does not exceed 108kW. For option (A): 40 speakers and 30 floodlights. Power usage for speakers = 40speakers×1.8kW/speaker=72kW. Power usage for floodlights = 30floodlights×2.2kW/floodlight=66kW. Total power usage for (A) = 72kW+66kW=138kW.
Eliminate Option (A): Since the total power usage for option (A) exceeds 108kW, we can eliminate option (A).
Calculate Power Usage: For option (B): 12 speakers and 54 floodlights.Power usage for speakers = 12 speakers ×1.8 kW/speaker = 21.6 kW.Power usage for floodlights = 54 floodlights ×2.2 kW/floodlight = 118.8 kW.Total power usage for (B) = 21.6 kW + 118.8 kW = 542 kW.
Eliminate Option (B): Since the total power usage for option (B) exceeds 108kW, we can eliminate option (B).
Calculate Power Usage: For option (C): 26 speakers and 13 floodlights.Power usage for speakers = 26 speakers ×1.8 kW/speaker = 46.8 kW.Power usage for floodlights = 13 floodlights ×2.2 kW/floodlight = 28.6 kW.Total power usage for (C) = 46.8 kW + 28.6 kW = 132 kW.
Check Budget for Option (C): The total power usage for option (C) is within the 108 kW limit. Now, let's check the budget for option (C).Cost for speakers = 26 speakers * $75/speaker = $1950.Cost for floodlights = 13 floodlights * $42/floodlight = $546.Total cost for (C) = $1950+$546=$2496.
Calculate Power Usage: Since the total cost for option (C) is within the budget of $3,300, option (C) meets both the power usage and budget requirements.
Eliminate Option (D): For option (D): 38 speakers and 22 floodlights.Power usage for speakers = 38 speakers ×1.8kW/speaker=68.4kW.Power usage for floodlights = 22 floodlights ×2.2kW/floodlight=48.4kW.Total power usage for (D) = 68.4kW+48.4kW=116.8kW.
Final Option: Since the total power usage for option (D) exceeds 108kW, we can eliminate option (D).
Final Option: Since the total power usage for option (D) exceeds 108kW, we can eliminate option (D).Option (C) is the only combination that meets both the power usage and budget requirements.
More problems from Interpret parts of quadratic expressions: word problems