Arianna 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.
To find the number of scarves Arianna can make when the area of each scarf is 5 square feet, we need to use the concept of inverse proportionality.
First, let's use the given information to form a relationship between the number of scarves (N) and the area of each scarf (A). We know that when the area of each scarf is 3 square feet, she can make 15 scarves.
So, we can write the equation:
N = k/A,
where k is the constant of proportionality.
Now, we can substitute the given values into the equation to solve for k.
When N = 15 and A = 3, we have:
15 = k/3.
To solve for k, we can cross multiply:
15 * 3 = k,
45 = k.
Now that we have the constant of proportionality (k = 45), we can use it to find the number of scarves when the area of each scarf is 5 square feet.
We substitute N = ?, A = 5, and k = 45 into the equation:
N = 45/5,
N = 9.
So, when the area of each scarf is 5 square feet, Arianna can make 9 scarves.
N is inversely proportional to A
so N*A=constant
N*A=3*15=45
if A becomes 5,N will be 45/5=9