7. Flora has a square fountain. It is a square fountain and she wants to place a walkway around it. The square fountain measures 4 meters on each side. The walkway will be one meter wide around the fountain.. a. Find the area of the walkway. b. One bag of colored stones covers 1 square meter, how many bags of stones will be needed to cover the entire walkway around the fountain? C. A bag of colored stones cost $24.99. How much will it cost to fill in he walkway with colored stones?

Respuesta :

Answer:

[tex]\begin{gathered} a)20m^2 \\ b)\text{ 20 bags of colored stones} \\ c)\text{ \$499.8} \end{gathered}[/tex]

Step-by-step explanation:

Since the square fountain measures 4 meters on each side and the walkway will be one meter wide, let's make a diagram to see the situation:

Then, to calculate the area of the walkway (green shaded region)

[tex]\begin{gathered} A_{total}=b\cdot h \\ A_{total}=6\cdot6=36m^2 \\ A_{founta\in}=4\cdot4=16m^2 \end{gathered}[/tex][tex]\begin{gathered} A_{walkway}=A_{total}-A_{fountain} \\ A_{walkway}=36-16=20m^2 \end{gathered}[/tex]

Now, how many colored stones will be needed if one bag covers 1 square meter:

There are 20 square meters on the walkway, then will be needed 20 bags of colored stones.

A bag of colored stones costs $24.99, then multiply 20 by $24.99:

[tex]20\cdot24.99=\text{ \$499.8}[/tex]

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