So today I was reading something in the paper and I noticed that the said the current value of the item was 6.47% less now than it was a year before and that its current value is $66500. Now, I vaguely recalled there was a way of figuring this out, but I didn't just want to look up the formula. I wanted to see if I could get to the formula myself and below are my initial steps. You see I've been recently seeking to improve my math skills so I've been starting off with algebra and have gotten up to playing around with quadratics. Prior to that, I was practicing rearranging equations.
Now, I knew how to reduce something by a given percent. Basically you take the value, and minus it by your value divided by 100 and multiplied by the percentage you wanted to reduce it by (I realise there's a simpler way of doing this but this came to mind initially so I just ran with it). So, I called this initial value a and created the formula below.
I then multiplied each side by 100, then applied the distributive law (ab - ac = a[b-c]) before finally dividing both sides by 100-6.47. This resulted in a being isolated, and thus gave me the formula. To reduce this formula even more, one could simply say you divide the current price by the percentage of its original value. In other words if a $56 is 25% off, you can find its value by doing 56/0.75 (it's current value is $56 and it is now 75% of its original value).
Anyways, I realise it's not all that impressive for most but I was pretty glad to have figured it out myself and further more to actually apply something I learnt.