MATH SOLVE

5 months ago

Q:
# PB and J ArrayKen has made a selection of square jam sandwiches for a party, which he arranges in a single layer on the table in a perfect rectangle. Sarah also bring the same number of sandwiches and places them in a single layer to form a border round kens sandwiches. Given that all sandwiches are used how many sandwiches could each person have made?Can someone help with this ASAP please. I need the answer too Read more on Brainly - https://brainly.com/sf/question/8797022

Accepted Solution

A:

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=10

A1=3*10=30

A2=30

total number of sandwiches of Ken------ > 30

total number of sandwiches of Sara------ > 30

2) x=4 and y=6

A1=4*6=24

A2=24

total number of sandwiches of Ken------ > 24

total number of sandwiches of Sara------ >24

1) x=3 and y=10

A1=3*10=30

A2=30

total number of sandwiches of Ken------ > 30

total number of sandwiches of Sara------ > 30

2) x=4 and y=6

A1=4*6=24

A2=24

total number of sandwiches of Ken------ > 24

total number of sandwiches of Sara------ >24