Question

alison, beatrice and chole each had some books. alison gave beatrice and chole some books that doubled the number of books they had, lastly chole gave alison and beatrice some books that doubled the number of books they had. each of them had 32 books at the end. how many books did each of them have at first?

Answer 1

alison, beatrice and chole each of them have at first 56, 8, 32 books.

alison, beatrice and chole each had some books. alison gave beatrice and chole some books that doubled the number of books they had, lastly chole gave alison and beatrice some books that doubled the number of books they had. each of them had 32 books at the end.

What is Working backward?

Working backward is process in which calculation done in reverse direction.

let alison, beatrice and chole has x,y and z books initially,

alison gave beatrice and chole some books that doubled the number of books they had
alison, beatrice and chole has (96-2y-2z), (2y) , (2z)
chole gave alison and beatrice some books that doubled the number of books they had. each of them had 32 books at the end.

alison, beatrice and chole has 2(96-2y-2z), 2(2y) , (96-2(96-2y-2z)-4y)

at the end,
beatrice = 32

4y=32

y = 8

chole =32

96-2(96-2y-2z)-4y)=32
z=32

alison = 96-y-z

x=96-8-32
x=56

Thus the required alison, beatrice and chole each of them have at first 56, 8, 32 books.

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