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A ball drops from a certain height. The height it will reach after reb

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New post 23 Feb 2017, 23:25
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A ball drops from a certain height. The height it will reach after rebounding from the floor is 80 percent of the previous height. The total travel is 3,104cm when it touches the floor on the third time. What is the value of the original height, in cm?

A. 400cm     
B. 500cm     
C. 600cm     
D. 700cm     
E. 800cm
[Reveal] Spoiler: OA

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Re: A ball drops from a certain height. The height it will reach after reb [#permalink]

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New post 24 Feb 2017, 00:26
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AustinKL wrote:
A ball drops from a certain height. The height it will reach after rebounding from the floor is 80 percent of the previous height. The total travel is 3,104cm when it touches the floor on the third time. What is the value of the original height, in cm?

A. 400cm     
B. 500cm     
C. 600cm     
D. 700cm     
E. 800cm


Let x be original height
total distance traveled => x + 2*0.8x + 2*0.64x = 3104
x + 1.6x + 1.28x = 3104
3.88x = 3104
x = 800

Hence option E is correct
Hit Kudos if you liked it 8-)

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Re: A ball drops from a certain height. The height it will reach after reb [#permalink]

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New post 24 Feb 2017, 08:49
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AustinKL wrote:
A ball drops from a certain height. The height it will reach after rebounding from the floor is 80 percent of the previous height. The total travel is 3,104cm when it touches the floor on the third time. What is the value of the original height, in cm?

A. 400cm     
B. 500cm     
C. 600cm     
D. 700cm     
E. 800cm


Let x be the ball's original height

So, x = distance of the ball's first DROP
And 0.8x = distance of the ball's first RISE
0.8x = distance of the ball's second DROP
(0.8)(0.8x) = distance of the ball's second RISE
(0.8)(0.8x) = distance of the ball's third DROP

At this point, the ball touches the ground for the third time.
So, the TOTAL distance = x + 0.8x + 0.8x + (0.8)(0.8x) + (0.8)(0.8x) = 3104 cm
Simplify: x + 0.8x + 0.8x + 0.64x + 0.64x = 3104 cm
Simplify: 3.88x = 3104
Solve: x = 800

Answer: E
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Re: A ball drops from a certain height. The height it will reach after reb [#permalink]

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New post 03 Oct 2017, 22:57
Can someone explain how come 0.64 x ?

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Re: A ball drops from a certain height. The height it will reach after reb [#permalink]

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New post 04 Oct 2017, 01:18
santro789 wrote:
Can someone explain how come 0.64 x ?


Every time the ball rebounds the next height will be 80% of previous height. So first time is x, second time is 80% of x, third time is 80% of second time (0.64)

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Re: A ball drops from a certain height. The height it will reach after reb   [#permalink] 04 Oct 2017, 01:18
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