# Math Help - Interesting Algebra (+indicies)

1. ## 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 2. Originally Posted by MattyD123 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? 3. Originally Posted by AllanCuz 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

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*

4. Originally Posted by MattyD123
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
My bad, I read $6 not$66. 75 is the correct answer. Second part seems correct as well.