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A furniture manufacturer produces chairs and sofas. Each chair requires 10 yards of fabric, and each sofa requires 20 yards of fabric. The manufacturer has 300 yards of fabric available. To fulfill orders, the number of sofas must be at least twice the number of chairs.

Let [tex]$x[tex]$[/tex] be the number of chairs and [tex]$[/tex]y$[/tex] be the number of sofas. Which inequalities are described in the problem? Check all that apply.

A. [tex]$y \geq 2x$[/tex]
B. [tex]$y \leq 2x$[/tex]
C. [tex]$10x + 20y \geq 300$[/tex]
D. [tex]$10x + 20y \leq 300$[/tex]



Answer :

GinnyAnswer
Let's break down the problem step by step to identify the inequalities that describe it.

1. Twice as many sofas as chairs:
- We are told that the manufacturer must produce at least twice as many sofas (\(y\)) as chairs (\(x\)).
- This can be expressed as the inequality \(y \geq 2x\).

2. Fabric constraints:
- Each chair requires 10 yards of fabric.
- Each sofa requires 20 yards of fabric.
- The total amount of fabric available is 300 yards.
- This can be expressed as \(10x + 20y \leq 300\).

To summarize, the inequalities that describe the given problem are:

- \(y \geq 2x\)
- \(10x + 20y \leq 300\)

So, we check these boxes:

- \(y \geq 2x\)
- \(10x + 20y \leq 300\)

The inequalities [tex]\(y \leq 2x\)[/tex] and [tex]\(10x + 20y \geq 300\)[/tex] do not correctly describe the constraints given in the problem.