Looks good to me.
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