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Ms. Johnston, the head librarian at the Grant County Library, can spend at most $\$3,200$ to expand the children's section of the library. When she buys from a particular discount seller, paperback books cost $\$2$ each and hardback books cost $\$22$ each. $\newline$ Select the inequality in standard form that describes this situation. Use the given numbers and the following variables. $\newline$ $x =$ the number of paperback books $\newline$ $y =$ the number of hardback books $\newline$ Choices: $\newline$ (A) $2x + 22y \leq 3,200$ $\newline$ (B) $2 + x + 22 + y \leq 3,200$ $\newline$ (C) $22 + x + 2 + y \leq 3,200$ $\newline$ (D) $22x + 2y \leq 3,200$

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Write a linear inequality: word problems

Full solution

Q. Ms. Johnston, the head librarian at the Grant County Library, can spend at most

\$3,200

to expand the children's section of the library. When she buys from a particular discount seller, paperback books cost

\$2

each and hardback books cost

\$22

each.

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of paperback books

\newline

y =

the number of hardback books

\newline

Choices:

\newline

(A)

2x + 22y \leq 3,200

\newline

(B)

2 + x + 22 + y \leq 3,200

\newline

(C)

22 + x + 2 + y \leq 3,200

\newline

(D)

22x + 2y \leq 3,200

Calculate Paperback Books Cost: Paperback books cost $\$2$ each, so the total cost for $x$ paperback books is $2x$ dollars.
Calculate Hardback Books Cost: Hardback books cost $\$22$ each, so the total cost for $y$ hardback books is $22y$ dollars.
Calculate Total Cost: The total cost for both paperback and hardback books is $2x + 22y$ dollars.
Determine Maximum Budget: Ms. Johnston can spend at most \$\(3\),\(200\), so the total cost must be less than or equal to \$\(3\),\(200\).
Formulate Inequality: The inequality that represents this situation is \(2x + 22y \leq 3,200\).

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