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The perimeter of a rectangular pool is more than 62 meters, and the width is at least 10 meters. Which system of inequalities represents the possible length in meters, [tex]\( l \)[/tex], and the possible width in meters, [tex]\( w \)[/tex], of the pool?

[tex]\[
\begin{aligned}
l + 2w & \geq 62 \\
w & \geq 10
\end{aligned}
\][/tex]

(Note: The original text had some repeated and incorrect inequalities. The corrected system of inequalities represents the conditions provided in the question.)

Sagot :

GinnyAnswer
Let's break down and solve the inequalities step-by-step to find the constraints on [tex]\( w \)[/tex] (the width of the rectangular pool). We are given the following system of inequalities:

1. [tex]\( w \leq 10 - 1 \)[/tex]
2. [tex]\( 21 + 2w \geq 62 \)[/tex]

First, let's solve each inequality individually.

Step 1: Solve [tex]\( w \leq 10 - 1 \)[/tex]

[tex]\[ w \leq 9 \][/tex]

So, the first constraint is [tex]\( w \leq 9 \)[/tex].

Step 2: Solve [tex]\( 21 + 2w \geq 62 \)[/tex]

First, isolate the term involving [tex]\( w \)[/tex]:

[tex]\[ 2w \geq 62 - 21 \][/tex]
[tex]\[ 2w \geq 41 \][/tex]

Next, solve for [tex]\( w \)[/tex] by dividing both sides by 2:

[tex]\[ w \geq \frac{41}{2} \][/tex]
[tex]\[ w \geq 20.5 \][/tex]

So, the second constraint is [tex]\( w \geq 20.5 \)[/tex].

Combining the Results:

We need [tex]\( w \leq 9 \)[/tex] and [tex]\( w \geq 20.5 \)[/tex] to hold simultaneously. However, examining these two inequalities shows that there are no values of [tex]\( w \)[/tex] that can simultaneously satisfy [tex]\( w \leq 9 \)[/tex] and [tex]\( w \geq 20.5 \)[/tex]. Hence, there is no range of [tex]\( w \)[/tex] values that satisfy both conditions together.

This inconsistency means that within the context of these constraints, there are no possible values for [tex]\( w \)[/tex] that can describe the width of the rectangular pool.
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