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

9 scarves.

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=(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=(k)/(A)`

`15=(k)/(3)`

`15*3=(k)/(3)*3`

`45=k`

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

`N=(45)/(5)`

`N=9`

Therefore, Ariana can make 9 scarves.