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Roger is going to purchase some writing instruments at the school store, where mechanical pencils cost $2\$2 and pens cost $1\$1. He can spend up to $8\$8, but not more.\newlineSelect the inequality in standard form that describes this situation. Use the given numbers and the following variables.\newlinex=x = the number of mechanical pencils Roger will buy\newliney=y = the number of pens Roger will buy\newline\newlineChoices:\newline(A) 2x+y82x + y \geq 8\newline(B) 2x+y82x + y \leq 8\newline(C) x+2y8x + 2y \leq 8\newline(D) x+2y8x + 2y \geq 8

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Q. Roger is going to purchase some writing instruments at the school store, where mechanical pencils cost $2\$2 and pens cost $1\$1. He can spend up to $8\$8, but not more.\newlineSelect the inequality in standard form that describes this situation. Use the given numbers and the following variables.\newlinex=x = the number of mechanical pencils Roger will buy\newliney=y = the number of pens Roger will buy\newline\newlineChoices:\newline(A) 2x+y82x + y \geq 8\newline(B) 2x+y82x + y \leq 8\newline(C) x+2y8x + 2y \leq 8\newline(D) x+2y8x + 2y \geq 8
  1. Calculate mechanical pencils cost: Mechanical pencils cost $2\$2 each, so if Roger buys xx mechanical pencils, the cost is 2x2x dollars.
  2. Calculate pens cost: Pens cost $1\$1 each, so if Roger buys yy pens, the cost is yy dollars.
  3. Set spending limit: Roger can spend up to $8\$8, so the total cost of mechanical pencils and pens should be less than or equal to $8\$8.
  4. Formulate inequality: The inequality that represents this situation is 2x2x (cost of mechanical pencils) plus yy (cost of pens) should be less than or equal to 88. So, 2x+y82x + y \leq 8.

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