Learn about More percent problems

Khan Academy Presents: Slightly harder percent problems

Learn about More percent problems Let say I go to a store and I have $50.00 in my wallet and at the store that day, they say it is a 25% off marked price sale. So 25% off marked price means that if the marked price is $100.00 the price I’m going to pay is going to be 25% less than a $100.00. So my question to you if I have $50.00 what is the highest marked price I can afford because I need to know that before I go finding something that I might like. So let’s do a little bit of algebra. So let x be the highest marked price that I can afford. So if the sale is 25% off of x, we could say that the sale price would be x -25% of x = the sale price and I’m assuming that I'm in a state without sales tax. Whatever the sale price is what I have to pay cash. So x-25% x = sale price, right the discount is can be 25% of x but we know that this is the same thing as x-.25x and we know that’s the same thing as—well because we know this is 1x, x is the same thing as 1x. 1x - .25x well that means that .75 x is equal to the sale price right. All I did is I rewrote x - 25%x as 1x - .25x and that’s the same thing as .75x. So .75x is going to be the sale price. Well what’s the sale price that I can afford? Well the sale price I can afford is $50.00, so .75x = $50.00 Anything, if x is any larger number than the number I’m solving for and the sale price is going to be more than $50.00 and I won’t be able to afford it so that’s how we set it. The highest I can pay is 50 and that’s the sale price. So going back to how we did this front of four we just divide both sides by. 75 and we say that the highest mark price that I can afford is 50/.75 and let’s figure out what that is, .75 goes into 50. Let’s add some zeroes in the back if I take this decimal move it to the right, take this decimal move it to the right, goes right there, so .75 goes on 50 the same number of times that 75 goes into 5000. So let’s do this, 75 goes in 50 zero times, 75 goes into 500. So let me think about that. I think it goes into it six times because 7 times can be too much. So 6 x 5 = 30, 6 x 7 = 42 + 3 = 45 so the remainder is 50, I see a pattern, bring down the zero well same thing again 75 goes into 500. 6 x 75 = 450 again and we’re going to go keep having that same pattern over and over and over again so it’s actually 66.66 I hope you don’t think I'm an evil person because of this number that happen to show up but anyway, so the highest sale price that I can afford or the highest marked price I can afford is $66.00 and if I were to round up and 67 cents if I were to round to the nearest penny. If I were to write this kind of as a repeating decimal I can write this is 66.66 repeating or I also know that .6666 going on forever is the same thing as 2/3 so it’s 66 2/3. But since we’re working with money and we’re working with dollars we should just round to the nearest penny so the highest marked price that I can afford is $66.67. So if I go I see a nice pair of shoes for $55.00 I can afford it. If I see a nice tie for $70.00 I can't afford it with the $50.00 in my pocket. So hopefully this not only will this teach you a little bit in math but it will help you do a little bit shopping. So let me ask you another problem, a very interesting problem. Let’s say I start with $100.00 and after one year it grows by 25% and then the next year, year 2 it shrinks by 25% so this could happen in the stock market. The first year I have a good year, my portfolio grows by 25%, the second I have a bad year and then my portfolio shrinks by 25%. So my question is how much money do I have at the end of the two years? Well a lot of people might say, “Oh this is easy so all if I grow by 25% and then I shrink by 25%, I’ll end up with the same amount of money but I’ll show you it’s actually not that simple because the 25% in either case or in both cases is actually a different amount of money. So let’s figure this out. If I start with a $100.00 and I grow it by 25%, 25% of 100 is $25.00. So I grew by $25.00 so I go to a $125.00, right? So after one year of growing by 25% I end up with a $125.00 and now this $125.00 is going to shrink by 25%. So if something shrinks by 25% that means is just going to be .75% of what it was before right 1 - 25%, .75 x 125, and just in case you’re confuse. I don’t repeat it to much but if something shrinks by 25% it is now 75% of its original value. So 125 shrinks by 25% is now 75% of 125 or .75 = 9475 so it’s interesting. If I start with a $100.00 and it grows by 25% and then it shrinks by 25% I end up with less than I started with and I want you to think about why that happens because 25% on a 100 is the amount that I’m gaining. That’s a smaller number than the amount that I’m losing. I’m losing 25% on a 125, that’s pretty interesting don’t you think? And that’s actually very interesting when a lot of people compare or well actually I won’t go into a stock return and things but I think that should be a pretty interesting thing. You should try that out with other examples. Another interesting thing is for any percentage gain I use to think about how much you would have to lose, what percentage you would have to lose to end up where you started. That’s another interesting project to figure out. Maybe I’ll do that in the future presentation but anyway I think you’re now ready to do some of that those percent madness problems, hope you have fun. Bye.