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At a back-to-school sale at her favorite store, Alexa can purchase any pair of pants for $22\$22 and any shirt for $12\$12. Her parents tell her that she can spend at most $200\$200 on these school clothes.\newlineSelect the inequality in standard form that describes this situation. Use the given numbers and the following variables.\newlinex=x = the number of pairs of pants\newliney=y = the number of shirts\newlineChoices:\newline(A) 12x+22y≤20012x + 22y \leq 200\newline(B) 12x + 22y < 200\newline(C) 22x+12y≤20022x + 12y \leq 200\newline(D) 22x + 12y < 200

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Q. At a back-to-school sale at her favorite store, Alexa can purchase any pair of pants for $22\$22 and any shirt for $12\$12. Her parents tell her that she can spend at most $200\$200 on these school clothes.\newlineSelect the inequality in standard form that describes this situation. Use the given numbers and the following variables.\newlinex=x = the number of pairs of pants\newliney=y = the number of shirts\newlineChoices:\newline(A) 12x+22y≤20012x + 22y \leq 200\newline(B) 12x+22y<20012x + 22y < 200\newline(C) 22x+12y≤20022x + 12y \leq 200\newline(D) 22x+12y<20022x + 12y < 200
  1. Determine cost per item: Determine the cost per item and set up the inequality. Alexa can buy pants for $22\$22 each and shirts for $12\$12 each. She can spend at most $200\$200. Let xx be the number of pairs of pants and yy be the number of shirts. The total cost is the sum of the cost of pants and shirts, which is 22x22x for pants and 12y12y for shirts. The inequality will compare this sum to the maximum amount she can spend, which is $200\$200.
  2. Write the inequality: Write the inequality. Since Alexa can spend at most $200\$200, the total cost for pants and shirts must be less than or equal to $200\$200. The inequality that represents this situation is 22x22x (cost for pants) plus 12y12y (cost for shirts) is less than or equal to $200\$200. So, the inequality is 22x+12y≤20022x + 12y \leq 200.
  3. Match to given choices: Match the inequality to the given choices. The inequality we have found is 22x+12y≤20022x + 12y \leq 200. We need to find this inequality among the choices provided.
  4. Compare to choices: Compare the inequality to the choices. Choice (A) is 12x+22y≤20012x + 22y \leq 200, which is not correct because it swaps the prices of pants and shirts. Choice (B) is 12x + 22y < 200, which is also incorrect for the same reason and because it uses a strict inequality instead of a less than or equal to. Choice (C) is 22x+12y≤20022x + 12y \leq 200, which matches our inequality. Choice (D) is 22x + 12y < 200, which is incorrect because it uses a strict inequality. Therefore, the correct choice is (C).

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