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Ariana has a large piece of fabric that she wants to use to make some scarves. The number N of scarves she can make is inversely proportional to the area A of each scarf. If the area of each scarf is 3 square feet, then she can make 15 scarves. If the area of each scarf is 5 square feet, how many scarves can she make? Arianna can make _____ scarves.

Respuesta :

Answer:

9 scarves.

Step-by-step explanation:

We have been given that the number N of scarves Ariana can make is inversely proportional to the area A of each scarf.

We know that equation of two inversely proportional quantities in in form [tex]y=\frac{k}{x}[/tex], where, k is constant of variation and y is inversely proportional to x.

Let us find constant of variation using our given information.

[tex]N=\frac{k}{A}[/tex]

[tex]15=\frac{k}{3}[/tex]

[tex]15*3=\frac{k}{3}*3[/tex]

[tex]45=k[/tex]

Now, we will substitute [tex]A=5\text{ and }k=45[/tex] in our equation to solve for N.

[tex]N=\frac{45}{5}[/tex]

[tex]N=9[/tex]

Therefore, Ariana can make 9 scarves.

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