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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

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 108108 kilowatts (kW) (\mathrm{kW}) of power. It was determined that the main contributors to power usage, speakers and floodlights, use 1.8 kW 1.8 \mathrm{~kW} and 2.2 kW 2.2 \mathrm{~kW} , respectively. Anouk also must keep within her budget of $3,300 \$ 3,300 . The rental company is charging $75 \$ 75 for each speaker and $42 \$ 42 for each floodlight. Which of the following combinations meets Anouk's requirements?\newlineChoose 11 answer:\newline(A) 4040 speakers and 3030 floodlights\newline(B) 12 12 speakers and 5454 floodlights\newline(C) 2626 speakers and 1313 floodlights\newline(D) 3838 speakers and 2222 floodlights

Full solution

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 108108 kilowatts (kW) (\mathrm{kW}) of power. It was determined that the main contributors to power usage, speakers and floodlights, use 1.8 kW 1.8 \mathrm{~kW} and 2.2 kW 2.2 \mathrm{~kW} , respectively. Anouk also must keep within her budget of $3,300 \$ 3,300 . The rental company is charging $75 \$ 75 for each speaker and $42 \$ 42 for each floodlight. Which of the following combinations meets Anouk's requirements?\newlineChoose 11 answer:\newline(A) 4040 speakers and 3030 floodlights\newline(B) 12 12 speakers and 5454 floodlights\newline(C) 2626 speakers and 1313 floodlights\newline(D) 3838 speakers and 2222 floodlights
  1. Calculate Power Usage: First, let's calculate the total power usage for each combination to ensure it does not exceed 108kW108 \, \text{kW}. For option (A): 4040 speakers and 3030 floodlights. Power usage for speakers = 40speakers×1.8kW/speaker=72kW40 \, \text{speakers} \times 1.8 \, \text{kW/speaker} = 72 \, \text{kW}. Power usage for floodlights = 30floodlights×2.2kW/floodlight=66kW30 \, \text{floodlights} \times 2.2 \, \text{kW/floodlight} = 66 \, \text{kW}. Total power usage for (A) = 72kW+66kW=138kW72 \, \text{kW} + 66 \, \text{kW} = 138 \, \text{kW}.
  2. Eliminate Option (A): Since the total power usage for option (A) exceeds 108kW108 \, \text{kW}, we can eliminate option (A).
  3. Calculate Power Usage: For option (B): 1212 speakers and 5454 floodlights.\newlinePower usage for speakers = 1212 speakers ×\times 1.81.8 kW/speaker = 21.621.6 kW.\newlinePower usage for floodlights = 5454 floodlights ×\times 2.22.2 kW/floodlight = 118.8118.8 kW.\newlineTotal power usage for (B) = 21.621.6 kW + 118.8118.8 kW = 545422 kW.
  4. Eliminate Option (B): Since the total power usage for option (B) exceeds 108kW108\,\text{kW}, we can eliminate option (B).
  5. Calculate Power Usage: For option (C): 2626 speakers and 1313 floodlights.\newlinePower usage for speakers = 2626 speakers ×\times 1.81.8 kW/speaker = 46.846.8 kW.\newlinePower usage for floodlights = 1313 floodlights ×\times 2.22.2 kW/floodlight = 28.628.6 kW.\newlineTotal power usage for (C) = 46.846.8 kW + 28.628.6 kW = 131322 kW.
  6. Check Budget for Option (C): The total power usage for option (C) is within the 108 kW108 \text{ kW} limit. Now, let's check the budget for option (C).\newlineCost for speakers = 2626 speakers * $75/speaker\$75/\text{speaker} = $1950\$1950.\newlineCost for floodlights = 1313 floodlights * $42/floodlight\$42/\text{floodlight} = $546\$546.\newlineTotal cost for (C) = $1950+$546=$2496\$1950 + \$546 = \$2496.
  7. Calculate Power Usage: Since the total cost for option (C) is within the budget of $3,300\$3,300, option (C) meets both the power usage and budget requirements.
  8. Eliminate Option (D): For option (D): 3838 speakers and 2222 floodlights.\newlinePower usage for speakers = 3838 speakers ×1.8kW/speaker=68.4kW\times 1.8 \, \text{kW/speaker} = 68.4 \, \text{kW}.\newlinePower usage for floodlights = 2222 floodlights ×2.2kW/floodlight=48.4kW\times 2.2 \, \text{kW/floodlight} = 48.4 \, \text{kW}.\newlineTotal power usage for (D) = 68.4kW+48.4kW=116.8kW68.4 \, \text{kW} + 48.4 \, \text{kW} = 116.8 \, \text{kW}.
  9. Final Option: Since the total power usage for option (D) exceeds 108kW108 \, \text{kW}, we can eliminate option (D).
  10. Final Option: Since the total power usage for option (D) exceeds 108kW108\,\text{kW}, we can eliminate option (D).Option (C) is the only combination that meets both the power usage and budget requirements.

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