Quandaries
and Queries 

I'm having trouble figuring out how to figure a percentage??? it's easy to find what 40% of any given number is, but how would i accurately figure out what is the final number is when i know the number after the 40% has been removed? when i add 40% to this number it obviously is lower than it should be. the best i could figure is; x=?40% > x?=40% i'm all confused???? any help would be greatly appreciated. Thanks much 

Hi Cathy, Think of what you do in the "forward" direction. If you have $250 and you want to remove 40% of it you have
Now suppose that you buy something at a shop for $150 and you know that the original price of this item was reduced by 40% to arrive at the $150. If the original price was $x then, looking at the equation above, the shopkeeper calculated
To find x, divide both sides by 0.6 to get
A similar argument works if you want to add 40%. Suppose you bought an item for $420 and you know that the shopkeeper's markup is 40%. Then the shopkeeper took her price, $x, and multiplied by 1.4 to get the $300 price. That is
Thus
So the shopkeeper paid $300 for the item. Penny 

