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Amelia is designing an exhibit of her paintings and has at most 214214 square feet of wall space on which to display them. Her small paintings take up 55 square feet each, and her larger paintings take up 2121 square feet each.\newlineSelect the inequality in standard form that describes this situation. Use the given numbers and the following variables.\newlinex=x = the number of small paintings\newliney=y = the number of large paintings\newlineChoices:\newline(A) 5x+21y≤2145x + 21y \leq 214\newline(B) 5x+21y≥2145x + 21y \geq 214\newline(C) 21x+5y≤21421x + 5y \leq 214\newline(D) 21x+5y≥21421x + 5y \geq 214

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Q. Amelia is designing an exhibit of her paintings and has at most 214214 square feet of wall space on which to display them. Her small paintings take up 55 square feet each, and her larger paintings take up 2121 square feet each.\newlineSelect the inequality in standard form that describes this situation. Use the given numbers and the following variables.\newlinex=x = the number of small paintings\newliney=y = the number of large paintings\newlineChoices:\newline(A) 5x+21y≤2145x + 21y \leq 214\newline(B) 5x+21y≥2145x + 21y \geq 214\newline(C) 21x+5y≤21421x + 5y \leq 214\newline(D) 21x+5y≥21421x + 5y \geq 214
  1. Identify Variables: Amelia has at most 214214 square feet of wall space for her paintings. We need to find an inequality that represents the maximum amount of wall space used by the small and large paintings combined. The variable xx represents the number of small paintings, each taking up 55 square feet, so the total space used by small paintings is 5x5x square feet.
  2. Calculate Space Used: The variable yy represents the number of large paintings, each taking up 2121 square feet, so the total space used by large paintings is 21y21y square feet.
  3. Combine Small and Large Paintings: To find the total space used by both small and large paintings, we add the space used by small paintings 5x5x to the space used by large paintings 21y21y, which gives us 5x+21y5x + 21y square feet.
  4. Formulate Inequality: Since Amelia has at most 214214 square feet of wall space, the total space used by the paintings cannot exceed this amount. Therefore, the inequality that describes this situation is that the total space used by both small and large paintings must be less than or equal to 214214 square feet. The inequality is 5x+21y≤2145x + 21y \leq 214.

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