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.
15*3=5*A
so A=5
To find the number of scarves Arianna can make when the area of each scarf is 5 square feet, we need to determine the relationship between the number of scarves and the area.
The problem states that the number N of scarves Arianna can make is inversely proportional to the area A of each scarf. This means that as the area increases, the number of scarves decreases, and vice versa.
We are given that when the area of each scarf is 3 square feet, Arianna can make 15 scarves. We can use this information to set up an equation to solve for the constant of proportionality, k.
The equation for inverse proportionality is N = k/A. Plugging in the values we know, 15 for N and 3 for A, we get:
15 = k/3.
To solve for k, we multiply both sides of the equation by 3:
15 * 3 = k.
k = 45.
Now that we have the value of k, we can use it to find the number of scarves when the area is 5 square feet. Plugging 5 into the equation, we get:
N = 45/5 = 9.
Therefore, Arianna can make 9 scarves when the area of each scarf is 5 square feet.
Arianna can make 9 scarves.
12 scarves.
If the number N of scarves she can make is inversely proportional to the area A of each scarf, then we have the equation:
N = x/A, where x is the total area of the large piece of fabric she uses
First, we need to calculate what is the total area of the large piece of fabric she uses (x):
It is given:
A = 4 square feet
N = 15
If N = x/A, then: x = A * N = 4 * 15 = 60 square feet
Now, we have to calculate the number of scarves she can make if the area of the scarf is 5 square feet.
So, it is given:
x = 60 square feet,
A = 5 square feet
If N = x/A, then: N = 60/5 = 12 scarves