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A carpenter is building shelving units for a garage. A small shelf requires a total of $7$ boards to build, while a large one uses $15$ boards. He has up to $48$ boards to use for this project. $\newline$ Select the inequality in standard form that describes this situation. Use the given numbers and the following variables. $\newline$ $x =$ the number of small shelving units $\newline$ $y =$ the number of large shelving units $\newline$ Choices: $\newline$ (A) $7x + 15y \leq 48$ $\newline$ (B) $7x - 15y \geq 48$ $\newline$ (C) $7x + 15y \geq 48$ $\newline$ (D) $7x + 15y \leq 48$

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Write a linear inequality: word problems

Full solution

Q. A carpenter is building shelving units for a garage. A small shelf requires a total of

7

boards to build, while a large one uses

15

boards. He has up to

48

boards to use for this project.

\newline

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

\newline

x =

the number of small shelving units

\newline

y =

the number of large shelving units

\newline

Choices:

\newline

(A)

7x + 15y \leq 48

\newline

(B)

7x - 15y \geq 48

\newline

(C)

7x + 15y \geq 48

\newline

(D)

7x + 15y \leq 48

Shelf Boards Breakdown: Small shelf boards: $7$ per unit. Large shelf boards: $15$ per unit. Total boards available: $48$ .
Variables Defined: Let $x$ be the number of small shelving units. $\newline$ Let $y$ be the number of large shelving units.
Total Boards Calculation: Total boards used by small shelves: $7x$ . Total boards used by large shelves: $15y$ .
Total Boards Limit: Total boards used: $7x + 15y$ . The carpenter can use up to $48$ boards.
Inequality Representation: Inequality representing the situation: $7x + 15y \leq 48$ .

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