Question

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.

Answer 1

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 $y=\frac{k}{x}$, where, k is constant of variation and y is inversely proportional to x.

Let us find constant of variation using our given information.

$N=\frac{k}{A}$

$15=\frac{k}{3}$

$15*3=\frac{k}{3}*3$

$45=k$

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

$N=\frac{45}{5}$

$N=9$

Therefore, Ariana can make 9 scarves.