Cathy sells twice as many pink sweaters as green sweaters each month. She averages 20 less green sweaters than pink sweaters each month. How many of each color sweater did Cathy sell?

Number of green sweaters = x

Number of pink sweaters = y = 2x

As per the question,

x = y - 20
=> x = 2x - 20
=> 20 = 2x - x
=> x = 20

So, x = 20, y = 40

p = 2g

g = p-20

now just solve for p and g.

Let's assign variables to represent the number of pink and green sweaters Cathy sells each month. Let's say "P" represents the number of pink sweaters and "G" represents the number of green sweaters.

According to the information provided, Cathy sells twice as many pink sweaters as green sweaters each month. So, we can write the equation: P = 2G.

It is also mentioned that Cathy averages 20 less green sweaters than pink sweaters each month. So, we can write another equation: G = P - 20.

Now we have a system of equations:

P = 2G (Equation 1)
G = P - 20 (Equation 2)

To find the values of P and G, we can solve this system of equations. Let's substitute Equation 2 into Equation 1:

P = 2(P - 20)

Simplifying the equation, we get:

P = 2P - 40

Rearranging the equation, we get:

P - 2P = -40

Simplifying further, we get:

-1P = -40

Multiplying both sides of the equation by -1, we get:

P = 40

Now we can substitute this value into Equation 2 to find G:

G = 40 - 20

G = 20

Therefore, Cathy sold 40 pink sweaters and 20 green sweaters.