Originally Posted by

**Soroban** Hello, Helena!

There's some information missing.

I'll take a *guess* at what it is.

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

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

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

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

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

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

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