Ken has made a selection of square jam sandwiches for a party which you ranges in a single layer on the table in a perfect rectangle sarah has brought along the same number of square peanut butter sandwiches which she puts out also a single layer to form a board at one sandwich wide around cans rectangle given that all the sandwiches are the same size and they all use how many sandwiches could each person possibly have made

Let
x----------> number of  square jam sandwiches of Ken in the side x of rectangle
y---------> number of  square jam sandwiches of Ken in the side y of rectangle
A1-------------> total number of  square jam sandwiches of Ken
A2-------------> total number of  square jam sandwiches of Sara
we know that
A1=xy
A2=[(x+2)(y+2)-xy]
A1=A2
xy=[(x+2)(y+2)]-xy------------ > xy=xy+2x+2y+4-xy
xy-2y=2x+4-------- > y=[2x+4]/[x-2]
testing different values of x to get a pair of whole numbers--> see the table attached I find 2 solutions 1)  x=3  and y=10A1=3*10=30A2=30total number of sandwiches of Ken------ >  30total number of sandwiches of Sara------ > 30 
2) x=4  and y=6A1=4*6=24A2=24total number of sandwiches of Ken------ > 24total number of sandwiches of Sara------ >24

The first one, i believe, would be correct. all the others have one thing in common, and that's that they have repeating numbers. in the second one, x and y have repeating 6's and 3's, and in the third, x and y have repeating 6's as well. in the last one, there are repeating 3's. the first one has no repeating numbers.