SOLUTION: Karen spent all but $8.00 of her savings in three stores. In each store she spent $2.00 less than half of what she had when she went in. How much money did Karen have at the star

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Karen spent all but $8.00 of her savings in three stores. In each store she spent $2.00 less than half of what she had when she went in. How much money did Karen have at the star      Log On


   

Question 42781: Karen spent all but $8.00 of her savings in three stores. In each store she spent $2.00 less than half of what she had when she went in. How much money did Karen have at the start?
Answer by venugopalramana(3286) About Me  (Show Source):
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LET KAREN HAVE AT THE BEGINNING……X ….HENCE SHE SPENT X-8……MONEY REMAINING =8
STORE 1…….SHE HAD AT START X …HALF OF IT =X/2…..2 LESS THAN THAT =0.5X-2…SO SHE SPENT =0.5X-2….REMAINING=X-0.5X+2=0.5X+2
STORE 2…….SHE HAD AT START 0.5X+2 …HALF OF IT =0.25X+1…..2 LESS THAN THAT =0.25X+1-2…SO SHE SPENT =0.25X-1….REMAINING=0.5X+2-0.25X+1=0.25X+3
STORE 3…….SHE HAD AT START 0.25X+3 …HALF OF IT =0.125X+1.5…..2 LESS THAN THAT =0.125X+1.5-2…SO SHE SPENT =0.125X-0.5….REMAINING=0.25X+3-0.125X+0.5=0.125X+3.5
HENCE WE HAVE ……0.125X+3.5=8….OR……..0.125X=4.5……….
X=36