Question

Rahul, a developer is creating a plan for a park which is of 44 acres. It includes a 4-acre lake which cannot be developed. He later realizes that 8 to 10 acres, inclusive, needs to be reserved for soccer fields. Determine the inequality which correctly shows the amount of land (p)within the park that is available for development.
A. \[26 \le p \le 40\]
B. \[30 \le p \le 32\]
C. \[34 \le p \le 36\]
D. \[36 \le p \le 40\]

Answer 1

Hint: Here, the question is asked to find the remaining area for the development after removing the 4 acres for lake, and 8 to 10 acres for the soccer field. So it is quite simple to find the remaining area to develop, we have to subtract the both areas of lake and soccer field from the total area.


Complete step by step solution
Given:
The total area of the park that needs to develop a plan is \[p = 44\,{\rm{acres}}\].
The amount of land that includes a lake which cannot be developed is \[l = 4\,{\rm{acre}}\].
The amount of land that is reserved for the soccer field is \[s = 8\;{\rm{acres to }}10\;{\rm{acres}}\].
We know the equation to find the remained land after removing the lake area is given by,
\[x = p - l\]
On substituting the values in the above equation, we get,
\[\begin{array}{c}
x = p - l\\
 = 44 - 4\\
 = 40\,{\rm{acres}}
\end{array}\]
Therefore, the land remaining after removing the lake area is 40 acres.
We know the equation to find the remaining land after realized that 8 to 10 acres is reserved for soccer field is,
\[y = x - s\]
On substituting the values in the above equation, we get,
\[\begin{array}{c}
y = x - s\\
 = 40 - 8\\
 = 32\,{\rm{acres}}
\end{array}\]
And,
\[\begin{array}{c}
y = x - s\\
 = 40 - 10\\
 = 30\,{\rm{acres}}
\end{array}\]
Therefore, the land remaining after removing the soccer field area is 30 to 32 acres.
It means, according to the result we got, the inequality that the amount of land within the park that is available for the development is\[30 \le p \le 32\].
Therefore, the inequality is \[30 \le p \le 32\], it means the option (b) is correct.


Note: Here, we need to keep in mind that the soccer field area is not constant, it is given as 8 to 10 acres so according to the question we also cannot get the answer particularly, so we have to answer It in inequality form. It means the area to develop will lie between the inequality that we found.