# Pumpkin Problem

• Nov 17th 2012, 11:23 AM
dfung787
Pumpkin Problem
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

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 http://www.freemathhelp.com/forum/im...icon_smile.gif
• Nov 17th 2012, 11:38 AM
MarkFL
Re: Pumpkin Problem
Looks good to me. :)
• Nov 17th 2012, 12:06 PM
dfung787
Re: Pumpkin Problem
Thanks!