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Math Help - rate & amount

  1. #1
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    rate & amount

    1. The electricity costs of a business decreased from $12,000 one year to $10,920 the next. What is the rate of decrease?





    2. If the total bill at a restaurant, including a 15% tip, is $65.32, what was the cost of the meal alone?
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  2. #2
    Super Member Aryth's Avatar
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    Quote Originally Posted by Patience View Post
    1. The electricity costs of a business decreased from $12,000 one year to $10,920 the next. What is the rate of decrease?





    2. If the total bill at a restaurant, including a 15% tip, is $65.32, what was the cost of the meal alone?
    1. $12,000 - $10,920 = $1080

    $12000n = $1080

    n = .09

    Thus it is a 9% decrease.

    2. Some number a is the original price, so that:

    .15(a) + a = $65.32

    1.15a = $65.32

    a = $56.80

    To double check:

    $56.80 x .15 = $8.52 <-- That is our tip

    $56.80 + $8.52 = $65.32 <-- The price we had before.

    So it checks out.

    Basically I just used the percent equations:

    (Original Value) x n = (New Value)

    Which says that some percent n of the original value is the new value.
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Patience View Post
    1. The electricity costs of a business decreased from $12,000 one year to $10,920 the next. What is the rate of decrease?





    2. If the total bill at a restaurant, including a 15% tip, is $65.32, what was the cost of the meal alone?
    1. The electricity costs of a business decreased from $12,000 one year to $10,920 the next. What is the rate of decrease?

    Using A = Ao*e^rt ............where A is the amount after time t, Ao is the initial amount, r is the rate (in this case, the rate of decrease) and t is the time.

    => 10920 = 12000e^r after 1 year
    => 10920/12000 = e^r
    => 0.91 = e^r
    => r = ln0.91 = -0.094


    2. If the total bill at a restaurant, including a 15% tip, is $65.32, what was the cost of the meal alone?

    recall that percentage is just a fancy word for "/100" so 15% means 15/100 = 0.15
    also recall that in math, "of" means multiply. so 15% of something means 0.15*something. now moving on

    Let x be the cost of the meal alone.
    So we pay the cost of the meal, plus 15% of the cost of the meal as a tip. so our total cost, which is 65.32 is given by:

    65.32 = x + 0.15x = 1.15x
    => 65.32/1.15 = x
    => x = 56.80

    so the cost of the meal is $56.80
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Aryth View Post
    1. $12,000 - $10,920 = $1080

    $12000n = $1080

    n = .09

    Thus it is a 9% decrease.
    so this is a simpler method for number 1, i dont know why i make things so complicated sometimes. do you even know the formula A = Ao*e^rt ?
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