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Ms. Ellis, the head librarian at the Marshall County Library, can spend at most $3,300\$3,300 to expand the children's section of the library. When she buys from a particular discount seller, paperback books cost $2\$2 each and hardback books cost $14\$14 each.\newlineSelect the inequality in standard form that describes this situation. Use the given numbers and the following variables.\newlinex=x = the number of paperback books\newliney=y = the number of hardback books\newlineChoices:\newline(A) 14x+2y≥3,30014x + 2y \geq 3,300\newline(B) 2x+14y≥3,3002x + 14y \geq 3,300\newline(C) 2x+14y≤3,3002x + 14y \leq 3,300\newline(D) 14x+2y≤3,30014x + 2y \leq 3,300

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Q. Ms. Ellis, the head librarian at the Marshall County Library, can spend at most $3,300\$3,300 to expand the children's section of the library. When she buys from a particular discount seller, paperback books cost $2\$2 each and hardback books cost $14\$14 each.\newlineSelect the inequality in standard form that describes this situation. Use the given numbers and the following variables.\newlinex=x = the number of paperback books\newliney=y = the number of hardback books\newlineChoices:\newline(A) 14x+2y≥3,30014x + 2y \geq 3,300\newline(B) 2x+14y≥3,3002x + 14y \geq 3,300\newline(C) 2x+14y≤3,3002x + 14y \leq 3,300\newline(D) 14x+2y≤3,30014x + 2y \leq 3,300
  1. Calculate cost per item: Determine the cost per item for each type of book. We are given that paperback books cost $2\$2 each and hardback books cost $14\$14 each. The number of paperback books is represented by xx, and the number of hardback books is represented by yy. Therefore, the total cost for paperback books is 2x2x and the total cost for hardback books is 14y14y.
  2. Form total expenditure expression: Combine the costs to form an expression for the total expenditure. The total cost for both paperback and hardback books is the sum of the cost for each type of book, which is 2x2x for paperbacks and 14y14y for hardbacks. So, the total cost is 2x+14y2x + 14y.
  3. Apply budget constraint: Apply the budget constraint to the total cost. Ms. Ellis can spend at most $3,300\$3,300 on books. This means that the total cost for both types of books must be less than or equal to $3,300\$3,300. Therefore, the inequality that represents this situation is 2x+14y≤3,3002x + 14y \leq 3,300.

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