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

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27-02-2018
Mathematics

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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

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calculista calculista · Answer 1 · 2018-03-09T02:45:46+01:00

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