A product has undergone two price increases with the same percentage, ie by x percent each time. How big was the increase in percent each time?
( 1 ) The total price increase was 450 dollars
(2) After the two price increases, the price of the product went from 800 dollars to 1250 dollars
The answer is that we can solve this by only using statement (2). Could anyone show how to formulate this with equations? And why can't we solve it by using statement 1???
Let's say the relative increase is $x$. ( OBS not exactly the same as saying x % increase! )
1) Would give us $$(x-1) \cdot P + (x^2-1) \cdot P = 450$$ Two unknowns and 1 equation. Basically if the product was cheap there could be a larger percentage increase to add up to $450$ and if it was expensive it could have been a smaller percentage increase.
2) Would give us $$P = 800 \\(x-1) \cdot P + (x^2-1) \cdot P = 1250-800 = 450$$
Now as we know $P$, we are left with solving the second degree polynomial in $x$. This we can do. But as it is a second degree polynomial it could have several solutions we need to check.