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Math Help - Interesting Algebra (+indicies)

  1. #1
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    Interesting Algebra (+indicies)

    Hello, looking for help with the following two questions.

    1) A bookshop is reducing the price of certain books by 12%.

    (i)Work out a formula linking the sale price of a book to its original price.

    (ii)If the sale price of a particular book is $66, what was its original price?

    2) Use the index laws to simplify the following.

    (i) a(9a^2 b)^2 / 3a^4 b^ 3
    (i) 4x^-2/y^-3 / xy^2 / 3x^-2

    Looking forward to collaborating to solve these issues.

    Thanks
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  2. #2
    Senior Member AllanCuz's Avatar
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    Quote Originally Posted by MattyD123 View Post
    Hello, looking for help with the following two questions.

    1) A bookshop is reducing the price of certain books by 12%.

    (i)Work out a formula linking the sale price of a book to its original price.
    New Price = .88(Old Price)
    (ii)If the sale price of a particular book is $66, what was its original price?
    $6.82
    2) Use the index laws to simplify the following.

    (i) a(9a^2 b)^2 / 3a^4 b^ 3
    (i) 4x^-2/y^-3 / xy^2 / 3x^-2

    Looking forward to collaborating to solve these issues.

    Thanks
    \frac{a(9a^2b)^2}{3a^4b^3} = \frac{27a}{b}

     \frac { \frac{4x^{-2} }{y^{-3} } }{ \frac{xy^3}{3x^{-2} } } = \frac {4x^{-2}(3x^{-2})}{y^{-3} (xy^3)} = ....

    Can you simplify the last one?
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  3. #3
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    Quote Originally Posted by AllanCuz View Post
    New Price = .88(Old Price)


    $6.82


    \frac{a(9a^2b)^2}{3a^4b^3} = \frac{27a}{b}

     \frac { \frac{4x^{-2} }{y^{-3} } }{ \frac{xy^3}{3x^{-2} } } = \frac {4x^{-2}(3x^{-2})}{y^{-3} (xy^3)} = ....

    Can you simplify the last one?
    Hi, thanks a lot for your help. I really appriciate it.

    For 1)(ii), I'm struggling to understand how you got the answer of 6.82. Here is what I got:

    • New Price = 0.88 * Old Price
    • Therefore: 66 = 0.88 * Old Price
    • Divide Both Sides by 0.88
    • Therefore: 75 = Old Price

    Please enlighten me.

    For 2) (ii) Here is what I got: 12/x^5

    edit: I'm glad everything is correct. Thank you for your very helpful and quick replies. You're a good person *thumbs up*
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  4. #4
    Senior Member AllanCuz's Avatar
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    Quote Originally Posted by MattyD123 View Post
    Hi, thanks a lot for your help. I really appriciate it.

    For 1)(ii), I'm struggling to understand how you got the answer of 6.82. Here is what I got:

    • New Price = 0.88 * Old Price
    • Therefore: 66 = 0.88 * Old Price
    • Divide Both Sides by 0.88
    • Therefore: 75 = Old Price
    Please enlighten me.

    For 2) (ii) Here is what I got: 12/x^5
    My bad, I read $6 not $66. 75 is the correct answer. Second part seems correct as well.

    Cheers
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