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Math Help - percentages

  1. #1
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    percentages

    Hi, this question has two parts so i will tell you part 1 first:
    A toy rabbit works using a single battery. When the battery is new, it has 250 units of power. After every hour of use the battery loses 20% of its remaining power.
    How many units of power remain in the battery after 2 hours?
    10% of 250= 25
    25 x 4= 100
    250 - 100= 150
    150 units remaining

    PART B

    The battery must have at least 100 units of power left for the toy rabbit to work.
    Show that the toy rabbit will still be working after 4 hours.

    i don't understand because, 100untis if from 2 hours so 100 x 2=200 = 4 hours
    250-200=50 but it needs at least 100units to work
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  2. #2
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    Quote Originally Posted by andyboy179 View Post
    Hi, this question has two parts so i will tell you part 1 first:
    A toy rabbit works using a single battery. When the battery is new, it has 250 units of power. After every hour of use the battery loses 20% of its remaining power.
    How many units of power remain in the battery after 2 hours?
    10% of 250= 25
    25 x 4= 100 20% per hour is not 40% in 2 hours
    250 - 100= 150
    150 units remaining

    PART B

    The battery must have at least 100 units of power left for the toy rabbit to work.
    Show that the toy rabbit will still be working after 4 hours.

    do i do another 2 hours from the 150 units left? or is it 4 hours from a new battery, 250untis?
    Hi andyboy179,

    A loss of 20% in the first hour loses 20% of 250, which is 50,
    leaving 200 units remaining after an hour.
    A loss of 20% in the second hour loses 20% of the remaining 200 units.

    Continue this process for the next 2 hours to answer the two questions.
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  3. #3
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    Quote Originally Posted by Archie Meade View Post
    Hi andyboy179,

    A loss of 20% in the first hour loses 20% of 250, which is 50,
    leaving 200 units remaining after an hour.
    A loss of 20% in the second hour loses 20% of the remaining 200 units.

    Continue this process for the next 2 hours to answer the question.

    but it says 1 hour loses 20%, 20%= 50 but it wants 2 hours so 50+50=100
    250-100=150
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  4. #4
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    sorry i get it now!!! so 20% of 200= 20
    50+20=70
    250-70=180

    now is where im stuck do i do 180-70=110 to get part be correct?
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  5. #5
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    Quote Originally Posted by andyboy179 View Post
    sorry i get it now!!! so 20% of 200= 20
    50+20=70
    250-70=180

    now is where im stuck do i do 180-70=110 to get part be correct?
    Pretty good but 20% of 200 = 200/5 = 40

    You can either take 40 from 200 or take (50+40) from 250. Both expressions equal 160 which is correct
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  6. #6
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    Quote Originally Posted by e^(i*pi) View Post
    Pretty good but 20% of 200 = 200/5 = 40

    You can either take 40 from 200 or take (50+40) from 250. Both expressions equal 160 which is correct
    thanks, but when i got 160 would i do 20% of that = 32
    160-32=128
    20%128= 25.6???
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  7. #7
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    Quote Originally Posted by andyboy179 View Post
    thanks, but when i got 160 would i do 20% of that = 32
    160-32=128
    20%128= 25.6???
    That's right.

    There is a formula for this if you don't want to show all the steps:

    P_t = P_0 \cdot 0.8^t

    Where
    • P_t = power at time t
    • P_0 = power at time 0 (250)
    • t = time
    • 0.8 = 1-0.2 where 0.2 is the 20% power loss


    For example at time 0:  P_t = 250 \cdot 0.8^0 = 250

    At time 1: P_t = 250 \cdot 0.8^1 = 200
    At time 2: P_t = 250 \cdot 0.8^2 = 160
    At time 3: P_t = 250 \cdot 0.8^3 = 128
    At time 4: P_t = 250 \cdot 0.8^4 = 102.4

    and so on
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