Question 163461
Derek brought raisins for lunch and shared them with some of his classmates.
 He gave half of his raisins to Molly then ate one himself. After that he gave
 half of the remaining to Tricia and ate another one himself. Finally, he gave
 half of the remaining raisins to Clark, and had 7 raising left.
 How many raisins did Derek start with?
;
Let x = no. of raisins to start with
:
x - .5x - 1;  Molly
(.5x-1); remaining
:
(.5x-1) - .5(.5x-1) - 1; Tricia
.5x - 1 - .25x + .5 - 1
.5x - .25x +.5 - 1 - 1
.25x - 1.5; remaining
:
(.25x-1.5) - .5(.25-1.5) - 1; Clark
.25x - 1.5 - .125 + .75 - 1
.25x - .125x - 1.5 + .75 - 1
.125x - 1.75 = 7; remaining
.125x = 7 + 1.75
.125x = 8.75
x = {{{8.75/.125}}}
x = 70 raisins to start with
:
:
Let's see if that flies:
70 - 35 - 1 = 34
34 - 17 - 1 = 16
16 - 8 - 1 = 7, hooray! it does