Question 63675: jose'and mike are members of a school wideo club. they were discussing sharing homemade videotapeds. when jose asked to borrow mike's videos, mike replied: "each video completely fills one videotape. i have just one videotape at home. however, i used to have lots of tapes. i gave 1/2 of my videotapes plus 1/2 a tape to joanne. i gave 1/2 of my remaning videotapes and 1/2 a tape to martiza. lastly, i gave 1/2 of my remaning videotapes and 1/2 a tape to jeff.
how could many videotapes did mike have originally? why could joanne, martiza, and jeff watch all of the videotapes that mike gave them?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! i gave 1/2 of my videotapes plus 1/2 a tape to joanne. i gave 1/2 of my remaning videotapes and 1/2 a tape to martiza. lastly, i gave 1/2 of my remaning videotapes and 1/2 a tape to jeff.
:
Let x = number of tapes Mike originally had
:
(.5x + .5) given to Joan
:
x - (.5x + .5) left
Simplify:
x - .5x - . 5
(.5x - .5) left
:
.5(.5x-.5) + .5 given to Matilda
Simplify
.25x - .25 + .5
.25x +.25 given to Matilda
:
(.5x - .5) - (25x+.25) left
.5x -.5 - .25x - .25
.25x -.75 left
:
.5(.25x -.75) + .5 given to Jef
.125x - .375 + .5
.125x + .125 given to Jef
:
(.25x - .75) - (.125x + .125) = 1 left
.25x - .75 - 125x - .125 = 1
.125x - .875 = 1
.125x = 1 + .875
x = 1.875/.125
x = 15 tapes Mike had originally
:
:
Check it:
15 originally
8 given to Joan (7.5+.5)
---
7 left
4 given to Matilda (3.5+.5)
---
3 left
2 give to Jef (1.5+.5)
---
1 left
:
"why could joanne, martiza, and jeff watch all of the videotapes that mike gave them?"
I guess because, of the tapes they received, none were actually half a tape
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