SOLUTION: A certain ball dropped from a height will bounce half the height of its previous bounce for the first two bounces. When the ball hits the floor the third time, it will have trave

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A certain ball dropped from a height will bounce half the height of its previous bounce for the first two bounces. When the ball hits the floor the third time, it will have trave      Log On


   



Question 1025209: A certain ball dropped from a height will bounce half the height of its previous bounce for the first two bounces. When the ball hits the floor the third time, it will have traveled a total of 35 feet. What height was the bomb dropped?
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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A certain ball dropped from a height will bounce half the height of its previous bounce for the first two bounces.
When the ball hits the floor the third time, it will have traveled a total of 35 feet. What height was the bomb dropped?
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Your guiding equation is

x+%2B+%28%281%2F2%29x+%2B+%281%2F2%29x%29+%2B+%28%281%2F4%29x+%2B+%281%2F4%29x%29%29 = 35.

Simplify it:

x+%2B+x+%2B+%281%2F2%29x = 35,   or

2.5x = 35.

Hence, x = 35%2F2.5 = 14 feet.