Can't figure this problem out for algebra 1. HELP?!

Question

Cat pens will require 6ft of space and and dogs need 24ft of space. Carlos and Carlita have up to 360ft available in the storage shed. They also have $1280 they earned from their last business venture, it will cost $32 dollars for a cat pen, and $80 dollars for a dog pen. How many pens should they build?

Answer 1

6C + 24D = 360 --> C + 4D = 60 <---- divides everything by 6

32C + 80D = 1280---> 2C + 5D = 80 <--- divides everything by 16

-3D = -40

D = 40/3 = 13 and 1/3

C + 4( 13 and 1/3) = 60

C + 4 ( 40/3) = 60

C + 160/3 = 60

3C + 160 = 180

3C = 20

C = 20/3 = 6 and 2/3

CHECK:

(6 and 2/3)*6 + (13 and 1/3)*24 =

(20/3)*6 + (40/3)* 24 =

40 + 320 = 360

(6 and 2/3)*32 + (13 and 1/3)*80 =

(20/3)*32 + (40/3)* 80 =

640/3 + 3200/3 =

3840/3 =

1280

6 and 2/3 = 20/3 cat pens

13 and 1/3 = 40/3 dog pens

the answer checks.

repost