1. ## [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

2. 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: . $x^2 + 6x - 720 \;=\;0$

3. Originally Posted by Soroban
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...)