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Emmett is purchasing chocolate truffles to use as party favors. To ensure there are enough for everyone, he needs to purchase at least 248248 pieces. Dark chocolate truffles come in boxes of 1010 pieces and milk chocolate truffles come in boxes of 2424 pieces.\newlineSelect the inequality in standard form that describes this situation. Use the given numbers and the following variables.\newlinex=x = the number of boxes of dark chocolate truffles\newliney=y = the number of boxes of milk chocolate truffles\newlineChoices:\newline(A) 10x + 24y > 248\newline(B) 24x + 10y > 248\newline(C) 24x+10y≥24824x + 10y \geq 248\newline(D) 10x+24y≥24810x + 24y \geq 248

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Q. Emmett is purchasing chocolate truffles to use as party favors. To ensure there are enough for everyone, he needs to purchase at least 248248 pieces. Dark chocolate truffles come in boxes of 1010 pieces and milk chocolate truffles come in boxes of 2424 pieces.\newlineSelect the inequality in standard form that describes this situation. Use the given numbers and the following variables.\newlinex=x = the number of boxes of dark chocolate truffles\newliney=y = the number of boxes of milk chocolate truffles\newlineChoices:\newline(A) 10x+24y>24810x + 24y > 248\newline(B) 24x+10y>24824x + 10y > 248\newline(C) 24x+10y≥24824x + 10y \geq 248\newline(D) 10x+24y≥24810x + 24y \geq 248
  1. Define Variables: Define the variables based on the given information.\newlineWe are given:\newlineNumber of dark chocolate truffles in one box: 1010 pieces\newlineNumber of milk chocolate truffles in one box: 2424 pieces\newlineEmmett's requirement: At least 248248 pieces\newlineLet xx be the number of boxes of dark chocolate truffles.\newlineLet yy be the number of boxes of milk chocolate truffles.
  2. Write Expression: Write an expression for the total number of truffles.\newlineThe total number of dark chocolate truffles is 1010 pieces per box times the number of boxes, which is 10x10x.\newlineThe total number of milk chocolate truffles is 2424 pieces per box times the number of boxes, which is 24y24y.\newlineSo, the total number of truffles is 10x+24y10x + 24y.
  3. Formulate Inequality: Formulate the inequality based on the requirement.\newlineEmmett needs to purchase at least 248248 pieces, so the total number of truffles must be greater than or equal to 248248.\newlineThe inequality that represents this situation is 10x+24y≥24810x + 24y \geq 248.
  4. Match with Choices: Match the inequality with the given choices.\newlineThe inequality we have formulated is 10x+24y≥24810x + 24y \geq 248, which corresponds to choice (D)(D) from the given options.

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