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Math Help - [SOLVED] Quadratic equation problem...URGENT

  1. #1
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    Exclamation [SOLVED] Quadratic equation problem...URGENT

    The cost of an anorak rose by 6 pounds. As a result a shop could buy fewer anoraks for 600 pounds.
    If the cost of the anorak was x pounds before the rise, fin expressions, in terms of x, for the number of anoraks which could be bought before and after the rise.
    Hence form an equation in x and show how is reduces to x^2 +6x-720=0
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  2. #2
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    Hello, Helena!

    There's some information missing.
    I'll take a guess at what it is.


    The cost of an anorak rose by $6.
    As a result, a shop could buy five fewer anoraks for $600.

    If the cost of the anorak was x dollars before the rise,
    find expressions, in terms of x, for the number of anoraks
    which could be bought before and after the rise.
    For $600, at x dollars each, we can buy: . \frac{600}{x} anoraks.

    For $600, at x+6 dollars each, we can buy: . \frac{600}{x+6} anoraks.



    Hence, form an equation in x
    and show how it reduces to: x^2 +6x-720\:=\:0

    . . \underbrace{\frac{600}{x+6}}_{\text{new number}}  \;=\; \underbrace{\frac{600}{x}}_{\text{old number}}\;\underbrace{ - \;\;5}_{\text{5 less}}


    Multiply by x(x+6)\!:\;\;600x \;=\;600(x+6) - 5x(x+6)

    . . . . . . . . . . . . . . . 600x \;=\;600x + 3600 - 5x^2 - 30x

    . . . . . . . . . . . . . . 5x^2 + 30x - 3600 \;=\;0


    . . . . . . Divide by 5: . x^2 + 6x - 720 \;=\;0

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  3. #3
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    Quote Originally Posted by Soroban View Post
    Hello, Helena!

    There's some information missing.
    I'll take a guess at what it is.


    For $600, at x dollars each, we can buy: . \frac{600}{x} anoraks.

    For $600, at x+6 dollars each, we can buy: . \frac{600}{x+6} anoraks.




    . . \underbrace{\frac{600}{x+6}}_{\text{new number}}  \;=\; \underbrace{\frac{600}{x}}_{\text{old number}}\;\underbrace{ - \;\;5}_{\text{5 less}}


    Multiply by x(x+6)\!:\;\;600x \;=\;600(x+6) - 5x(x+6)

    . . . . . . . . . . . . . . . 600x \;=\;600x + 3600 - 5x^2 - 30x

    . . . . . . . . . . . . . . 5x^2 + 30x - 3600 \;=\;0


    . . . . . . Divide by 5: . x^2 + 6x - 720 \;=\;0

    Thanks a lot for your help! I only have one question:
    Where do you get the 5 from?
    I'm not supposed to solve the equation mentioned until after I have derived the formula...so if you did it the other way around and got the 5 that way...is there an other way of doing it? (I'm not told that they can buy 5 in the question, so...)
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