Question 740795: Barbara bought a box of cookies and shared them with three of her friends. a)Barbara shared her cookies in the following way: She gave the first friend one half of the cookies in the box, plus one cookie extra. Her second friend also got one half of what was left plus one extra cookie. The third friend came along and was treated in the same way as the other two friends. At the end of this, Barbara had 4 cookies left. How many cookies were there in the box to start with?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Barbara bought a box of cookies and shared them with three of her friends.
a)Barbara shared her cookies in the following way:
let x = no. to start with
She gave the first friend one half of the cookies in the box, plus one cookie extra.
x - (.5x + 1)
x - .5 - 1
(.5x - 1) remain
:
Her second friend also got one half of what was left plus one extra cookie.
(.5x-1) - [.5(.5x-1) + 1]
.5x - 1 - (.25x-.5+1)
.5x - 1 - (.25x + .5)
.5x -.25x - .5 - 1
.25x - 1.5 remain
:
The third friend came along and was treated in the same way as the other two friends. At the end of this, Barbara had 4 cookies left.
(.25x-1.5) - [.5(.25x-1.5)+1] = 4
.25x - 1.5 - (.125x - .75 + 1) = 4
.25x - 1.5 - (.125x + .25) = 4
.25x - 1.5 - 1.25x - .25 = 4
.25x - 1.25x - 1.5 - .25 = 4
.125x - 1.75 = 4
.125x = 4 + 1.75
.125x = 5.75
x = 5.75/.125
x = 46 cookies to start with
:
:
Check this
1st: 46 - 23 - 1 = 22
2nd: 22 - 11 - 1 = 10
3rd: 10 - 5 - 1 = 4 left
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