Hello, I need help with the following problem:

The cost of 2 large pumpkins plus 1 medium-sized pumpkin is the same as the cost of 8 small pumpkins. One large pumpkin costs the same as 1 medium sized pumpkin plus 1 small pumpkin. How many small pumpkins can you buy for the prize of a large pumpkin?

I solved the problem but I want to make sure that I did it correctly:

Prices

x = large pumpkin

y = medium pumpkin

z = small pumpkin

"cost of 2 large pumpkins plus 1 medium-sized pumpkin is the same as the cost of 8 small pumpkins"

2x + y = 8z

"One large pumpkin costs the same as 1 medium sized pumpkin plus 1 small pumpkin"

x = y + z

Using the substitution method to solve this system of equations:

2x + y = 8z

2(y + z) + y = 8z

2y + 2z + y = 8z

3y = 6z

y = 2z

Using the previous answer,

x = y + z

x = (2y) + z

x = 3z

Answer: You can buy 3 small pumpkins for the price of one large pumpkin.

Is this correct guys?? Thanks for your help