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Ms. Fischer, the head librarian at the Lee County Library, can spend at most $4,700\$4,700 to expand the children's section of the library. When she buys from a particular discount seller, paperback books cost $1\$1 each and hardback books cost $5\$5 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) x+5y≤4,700x + 5y \leq 4,700\newline(B) x + 5y < 4,700\newline(C) 5x + y < 4,700\newline(D) 5x+y≤4,7005x + y \leq 4,700

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Q. Ms. Fischer, the head librarian at the Lee County Library, can spend at most $4,700\$4,700 to expand the children's section of the library. When she buys from a particular discount seller, paperback books cost $1\$1 each and hardback books cost $5\$5 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) x+5y≤4,700x + 5y \leq 4,700\newline(B) x+5y<4,700x + 5y < 4,700\newline(C) 5x+y<4,7005x + y < 4,700\newline(D) 5x+y≤4,7005x + y \leq 4,700
  1. Budget Calculation: Ms. Fischer has a budget of $4,700\$4,700 for expanding the children's section of the library. We need to find an inequality that represents the maximum amount she can spend on paperback and hardback books. The cost of paperback books is $1\$1 each, and the cost of hardback books is $5\$5 each. Let's denote the number of paperback books as xx and the number of hardback books as yy.
  2. Paperback Books Cost: The total cost of the paperback books can be calculated by multiplying the number of paperback books by their cost. Since each paperback book costs $1\$1, the total cost for xx paperback books is $1\$1 times xx, which is simply xx.
  3. Hardback Books Cost: Similarly, the total cost of the hardback books can be calculated by multiplying the number of hardback books by their cost. Since each hardback book costs $5\$5, the total cost for yy hardback books is $5\$5 times yy, which is 5y5y.
  4. Total Cost Calculation: Now, we need to combine the costs of paperback and hardback books to find the total cost. The total cost is the sum of the cost of paperback books and the cost of hardback books, which is x+5yx + 5y.
  5. Budget Inequality: Since Ms. Fischer can spend at most \$\(4\),\(700\), the total cost of the books must be less than or equal to \$\(4\),\(700\). This gives us the inequality \(x + 5y \leq 4,700\), which represents the maximum amount she can spend on the books without exceeding her budget.

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