Pumpkin Problem

[megadeth95]

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

 

[mmm4444bot]

Prices

x = large pumpkin
y = medium pumpkin
z = small pumpkin

Everything looks good, to me.


Perhaps, symbol definitions would be initially clearer with the word "price" in the definitions versus as a subheading:

x = large-pumpkin price

y = medium-pumpkin price

z = small-pumpkin price

 

[megadeth95]

Thanks!

 

[Deleted member 4993]

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

CORRECT.... nice work.

But you could have done it faster!

2x + y = 8z....................................................................(1)

x = y + z →

x - y = z....................................................................(2)

If you add (1) and (2), you get

(2x + y) + (x - y) = 8z + z

2x + y + x - y = 9z

3x = 9 z

x = 3z

 

[megadeth95]

thanks for the feedback subhotosh khan!