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Alvin is shopping for supplies for a coworker's retirement party. Regular sized boxes of forks contain enough for 1212 guests, while value-pack boxes contain enough for 2525 guests. In all, there must be at least enough forks for the 5454 guests who plan to attend.\newlineSelect the inequality in standard form that describes this situation. Use the given numbers and the following variables.\newlinex=x = the number of regular boxes of forks\newliney=y = the number of value-packs boxes of forks\newline\newlineChoices:\newline(A) 12+x+25+y≤5412 + x + 25 + y \leq 54\newline(B) 12x+25y≥5412x + 25y \geq 54\newline(C) 12x+25y≤5412x + 25y \leq 54\newline(D) 12+x+25+y≥5412 + x + 25 + y \geq 54

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Q. Alvin is shopping for supplies for a coworker's retirement party. Regular sized boxes of forks contain enough for 1212 guests, while value-pack boxes contain enough for 2525 guests. In all, there must be at least enough forks for the 5454 guests who plan to attend.\newlineSelect the inequality in standard form that describes this situation. Use the given numbers and the following variables.\newlinex=x = the number of regular boxes of forks\newliney=y = the number of value-packs boxes of forks\newline\newlineChoices:\newline(A) 12+x+25+y≤5412 + x + 25 + y \leq 54\newline(B) 12x+25y≥5412x + 25y \geq 54\newline(C) 12x+25y≤5412x + 25y \leq 54\newline(D) 12+x+25+y≥5412 + x + 25 + y \geq 54
  1. Determine Forks per Box: Determine the amount of forks provided by each type of box.\newlineRegular sized boxes provide enough forks for 1212 guests, so if Alvin buys xx regular boxes, they will provide enough forks for 12x12x guests.\newlineValue-pack boxes provide enough forks for 2525 guests, so if Alvin buys yy value-pack boxes, they will provide enough forks for 25y25y guests.
  2. Combine Forks from Both Boxes: Combine the forks provided by both types of boxes to find the total number of guests that can be served.\newlineThe total number of guests that can be served by xx regular boxes and yy value-pack boxes is 12x+25y12x + 25y.
  3. Formulate Inequality: Formulate the inequality based on the requirement that there must be at least enough forks for 5454 guests.\newlineSince Alvin needs to have at least enough forks for 5454 guests, the total number of guests that can be served by the purchased boxes must be greater than or equal to 5454.\newlineThe inequality that represents this situation is 12x+25y≥5412x + 25y \geq 54.
  4. Match with Choices: Match the correct inequality with the given choices.\newlineThe inequality we have found is 12x+25y≥5412x + 25y \geq 54, which corresponds to choice (B)(B).

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