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A furniture company is shipping cargo overseas on a container ship. A shorter container can hold 40,50040,500 pounds and a longer container can hold 58,80058,800 pounds. Together, all the containers must hold at least 504,000504,000 pounds, the weight of the cargo.\newlineSelect the inequality in standard form that describes this situation. Use the given numbers and the following variables.\newlinex=x = the number of shorter containers\newliney=y = the number of longer containers\newlineChoices:\newline(A) 40,500x+58,800y≥504,00040,500x + 58,800y \geq 504,000\newline(B) 40,500x+58,800y≤504,00040,500x + 58,800y \leq 504,000\newline(C) 58,800x+40,500y≤504,00058,800x + 40,500y \leq 504,000\newline(D) 58,800x+40,500y≥504,00058,800x + 40,500y \geq 504,000

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Q. A furniture company is shipping cargo overseas on a container ship. A shorter container can hold 40,50040,500 pounds and a longer container can hold 58,80058,800 pounds. Together, all the containers must hold at least 504,000504,000 pounds, the weight of the cargo.\newlineSelect the inequality in standard form that describes this situation. Use the given numbers and the following variables.\newlinex=x = the number of shorter containers\newliney=y = the number of longer containers\newlineChoices:\newline(A) 40,500x+58,800y≥504,00040,500x + 58,800y \geq 504,000\newline(B) 40,500x+58,800y≤504,00040,500x + 58,800y \leq 504,000\newline(C) 58,800x+40,500y≤504,00058,800x + 40,500y \leq 504,000\newline(D) 58,800x+40,500y≥504,00058,800x + 40,500y \geq 504,000
  1. Identify Weight Capacity: Identify the weight capacity of each type of container and the total weight requirement.\newlineShorter container capacity: 40,50040,500 pounds\newlineLonger container capacity: 58,80058,800 pounds\newlineTotal weight of cargo: 504,000504,000 pounds
  2. Define Variables: Define the variables for the number of containers.\newlinexx = the number of shorter containers\newlineyy = the number of longer containers
  3. Write Total Weight Inequality: Write the inequality that represents the total weight of the cargo in terms of the number of containers.\newlineTotal weight of cargo in shorter containers: 40,500x40,500x\newlineTotal weight of cargo in longer containers: 58,800y58,800y\newlineThe total weight must be at least 504,000504,000 pounds, so the inequality is:\newline40,500x+58,800y≥504,00040,500x + 58,800y \geq 504,000
  4. Check Choices: Check the choices given to match the inequality derived in Step 33.\newline(A) 40,500x+58,800y≥504,00040,500x + 58,800y \geq 504,000 matches the inequality we derived.\newline(B) 40,500x+58,800y≤504,00040,500x + 58,800y \leq 504,000 does not match because it suggests the total weight could be less than or equal to 504,000504,000 pounds, which is not the requirement.\newline(C) 58,800x+40,500y≤504,00058,800x + 40,500y \leq 504,000 does not match because the coefficients of xx and yy are swapped and it suggests the total weight could be less than or equal to 504,000504,000 pounds.\newline(D) 58,800x+40,500y≥504,00058,800x + 40,500y \geq 504,000 does not match because the coefficients of xx and yy are swapped.

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