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Gwen wants to replace the flooring in her house with a combination of carpet and hardwood flooring, but she cannot exceed a budget of $\$4,900$ . The carpet she likes has a cost of $\$9$ per square foot, and the hardwood flooring she likes has a cost of $\$3$ per square foot. $\newline$ Select the inequality in standard form that describes this situation. Use the given numbers and the following variables. $\newline$ $x =$ the amount of carpet $\newline$ $y =$ the amount of hardwood flooring $\newline$ $\newline$ Choices: $\newline$ (A) $3x + 9y \leq 4,900$ $\newline$ (B) $9x + 3y \leq 4,900$ $\newline$ (C) $9x + 3y \geq 4,900$ $\newline$ (D) $3x + 9y \geq 4,900$

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Write two-variable inequalities: word problems

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Q. Gwen wants to replace the flooring in her house with a combination of carpet and hardwood flooring, but she cannot exceed a budget of

\$4,900

. The carpet she likes has a cost of

\$9

per square foot, and the hardwood flooring she likes has a cost of

\$3

per square foot.

\newline

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

\newline

x =

the amount of carpet

\newline

y =

the amount of hardwood flooring

\newline

\newline

Choices:

\newline

(A)

3x + 9y \leq 4,900

\newline

(B)

9x + 3y \leq 4,900

\newline

(C)

9x + 3y \geq 4,900

\newline

(D)

3x + 9y \geq 4,900

Calculate Cost per Unit: Determine the cost per unit for each type of flooring. Gwen has chosen carpet that costs $\$9$ per square foot and hardwood flooring that costs $\$3$ per square foot.
Define Variables: Define the variables according to the problem. Let $x$ represent the amount of carpet in square feet and $y$ represent the amount of hardwood flooring in square feet.
Total Cost of Carpet: Write the expression for the total cost of the carpet. The total cost for the carpet is the cost per square foot multiplied by the number of square feet, which gives us $9x$ .
Total Cost of Hardwood Flooring: Write the expression for the total cost of the hardwood flooring. The total cost for the hardwood flooring is the cost per square foot multiplied by the number of square feet, which gives us $3y$ .
Form Budget Constraint: Combine the costs to form an inequality representing the budget constraint. Gwen cannot exceed a budget of $\$4,900$ , so the combined cost of carpet and hardwood flooring must be less than or equal to $\$4,900$ . This gives us the inequality $9x + 3y \leq 4,900$ .
Match with Choices: Match the derived inequality with the given choices. The correct inequality that represents Gwen's situation is $9x + 3y \leq 4,900$ , which corresponds to choice $(B)$ .

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