Craig is building a shelving unit to hold all of his shoes. A pair of work shoes takes up 2 square feet of space, and a pair of boots occupies 5 square feet. The total amount of shelving space taken up by all the shoes can be at most 57 square feet. Select the inequality in standard form that describes this situation. Use the given numbers and the following variables. x = the number of pairs of shoes y = the number of pairs of boots Choices: (A)5x + 2y ≤ 57 (B)2x + 5y < 57 (C)2x + 5y ≤ 57 (D)5x + 2y < 57

Determine Inequality: We need to determine the inequality that represents the maximum amount of shelving space Craig can use for his shoes and boots. We are given that a pair of work shoes takes up 2 square feet of space, and a pair of boots occupies 5 square feet. The total space is at most 57 square feet. Let's denote the number of pairs of shoes as x and the number of pairs of boots as y.Calculate Space Used: The total space taken up by the shoes is 2 square feet per pair times the number of pairs of shoes, which is 2x. Similarly, the total space taken up by the boots is 5 square feet per pair times the number of pairs of boots, which is 5y.Formulate Inequality: Adding these two expressions together gives us the total space used by both shoes and boots, which is 2x + 5y. Since the total space cannot exceed 57 square feet, the inequality representing this situation is 2x + 5y ≤ 57.Match with Choices: Now we need to match our inequality with one of the given choices. The correct inequality that matches our calculation is (C)2x + 5y ≤ 57, which states that the total space for shoes and boots must be less than or equal to 57 square feet.

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Craig is building a shelving unit to hold all of his shoes. A pair of work shoes takes up $2\,\text{square feet}$ of space, and a pair of boots occupies $5\,\text{square feet}$ . The total amount of shelving space taken up by all the shoes can be at most $57\,\text{square feet}$ . $\newline$ Select the inequality in standard form that describes this situation. Use the given numbers and the following variables. $\newline$ $x =$ the number of pairs of shoes $\newline$ $y =$ the number of pairs of boots $\newline$ Choices: $\newline$ (A) $5x + 2y \leq 57$ $\newline$ (B) 2x + 5y < 57 $\newline$ (C) $2x + 5y \leq 57$ $\newline$ (D) 5x + 2y < 57

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Algebra 1

Write two-variable inequalities: word problems

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Q. Craig is building a shelving unit to hold all of his shoes. A pair of work shoes takes up

2\,\text{square feet}

of space, and a pair of boots occupies

5\,\text{square feet}

. The total amount of shelving space taken up by all the shoes can be at most

57\,\text{square feet}

\newline

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

\newline

x =

the number of pairs of shoes

\newline

y =

the number of pairs of boots

\newline

Choices:

\newline

(A)

5x + 2y \leq 57

\newline

(B)

2x + 5y < 57

\newline

(C)

2x + 5y \leq 57

\newline

(D)

5x + 2y < 57

Determine Inequality: We need to determine the inequality that represents the maximum amount of shelving space Craig can use for his shoes and boots. We are given that a pair of work shoes takes up $2$ square feet of space, and a pair of boots occupies $5$ square feet. The total space is at most $57$ square feet. Let's denote the number of pairs of shoes as $x$ and the number of pairs of boots as $y$ .
Calculate Space Used: The total space taken up by the shoes is $2$ square feet per pair times the number of pairs of shoes, which is $2x$ . Similarly, the total space taken up by the boots is $5$ square feet per pair times the number of pairs of boots, which is $5y$ .
Formulate Inequality: Adding these two expressions together gives us the total space used by both shoes and boots, which is $2x + 5y$ . Since the total space cannot exceed $57$ square feet, the inequality representing this situation is $2x + 5y \leq 57$ .
Match with Choices: Now we need to match our inequality with one of the given choices. The correct inequality that matches our calculation is (C) $2x + 5y \leq 57$ , which states that the total space for shoes and boots must be less than or equal to $57$ square feet.