The perimeter of a rectangular pool is more than 62 meters, and the width is at least 10 meters less than the length. 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?
A. [tex]
\begin{aligned}
w &\leq 10-1 \\
21+2 w &\geq 62
\end{aligned}
[/tex]
B. [tex]w \leq 10-1[/tex]
[tex]2 l+2 w>62[/tex]
C. [tex]w \leq I-10[/tex]
[tex]2 l+2 w \geq 62[/tex]
D. [tex]w \leq 1-10[/tex]
[tex]2^{\prime}+2 w>62[/tex]
Answer (2)
The perimeter of the rectangular pool is more than 62 meters, which translates to the inequality 62"> 2 l + 2 w > 62 .
The width is at least 10 meters less than the length, which translates to the inequality w ≤ l − 10 .
Combining these two inequalities, we obtain the system of inequalities: 62 \end{cases}"> { w ≤ l − 10 2 l + 2 w > 62 .
Therefore, the correct system of inequalities is 62}"> w ≤ l − 10 2 l + 2 w > 62 .
Explanation
Problem Analysis Let's analyze the given problem. We are given two conditions:
The perimeter of a rectangular pool is more than 62 meters.
The width is at least 10 meters less than the length.
We need to find the system of inequalities that represents these conditions, where l is the length and w is the width of the pool.
Formulating Inequalities The perimeter of a rectangle is given by 2 l + 2 w . Since the perimeter of the pool is more than 62 meters, we can write the inequality:
62"> 2 l + 2 w > 62
The width is at least 10 meters less than the length, which means the width is less than or equal to the length minus 10. We can write this as:
w ≤ l − 10
System of Inequalities Combining these two inequalities, we get the following system of inequalities:
62 \end{cases}"> { w ≤ l − 10 2 l + 2 w > 62
Final Answer Comparing our system of inequalities with the given options, we see that the correct system is:
w ≤ l − 10 62"> 2 l + 2 w > 62
Examples
Understanding inequalities can help in various real-life situations. For example, if you are planning a garden and have a limited amount of fencing, you can use inequalities to determine the possible dimensions of the garden while staying within your fencing limit. Similarly, if you are trying to stay within a budget while shopping, inequalities can help you determine the possible quantities of items you can buy without exceeding your budget. This problem demonstrates how inequalities can be used to model constraints and find possible solutions in practical scenarios.
The system of inequalities representing the length ( l ) and width ( w ) of the pool is: 62 \end{cases}"> { w ≤ l − 10 2 l + 2 w > 62 .
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