These are the assumptions I am using: the dimensions give above are raw not finished dimensions; I'm using 1/2" seam allowances; she is looking for the size of material she needs rather than the finished pillow size.
Given these assumptions I first subtract my seam allowances because they will remain constant regardless of the size of the pillow therefore I'm looking at an initial size of fabric of 18x14. I will also need to subtract the seam allowances from the smaller pieces so I am looking at a piece that will be 14x?. I need to solve for the unknown.
Ratio analysis is done by comparing 18:14 = 14:x or another way of putting it is 18/14 = 14/x. Solving this equation I get 18x = 14(14) or 18x = 196 or x = 196/18 or x = 10.888 which I would round to 11.
Now I need to add back in my seam allowances so I end up with a piece of fabric that would be 15x12 to keep the same proportions as the original piece of fabric. In other words 19x15 is proportionally equal to 15x12