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:
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