If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content

# More percent problems

## Video transcript

let's say I go to a store and I have \$50 in my pocket \$50 in my wallet and at the store that day they say it is a 25% off marked price sale so 25% off mark price means that if the marked price is \$100 the price I'm going to pay is going to be 25% less than \$100 so my question to you is if I have \$50 what is the highest marked price I can afford because I need to know that before I go finding something that I that I might like so let's do a little bit of algebra so let X X be the highest marked price that I can afford so if the sale is 25% off of X we could say that the new price the sale price will be X minus 25% 25% of X is equal to the sale price and I'm assuming that I'm in a state without sales tax whatever the sale price is is what I have to pay cash so X minus 25% X is equal to sale price right the discount is going to be 25% of X well we know that this is the same thing as X minus 0.25 X and we know that that's the same thing as well because we know this is 1 X X is the same thing as 1 X 1 X minus 0.25 X well this that means that 0.75 X is equal to the sale price right all I did is I rewrote X minus 25% of X as 1 X minus 0.25 X and that's the same thing as 0.75 X right because 1 minus 0.25 is points five so 0.75 X 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 so 0.75 X is going to equal \$50 anything if X is any larger number than the number I'm solving for then the sale price is going to be more than \$50 and I won't be able to afford it so that's how we set the exam the the highest I can pay is 50 and that's the sale price so going back to how we did these problems before we just divide both sides by 0.75 and we say that the highest sales the highest marked price that I can afford is 50 divided by 0.75 and let's figure out what that is 0.75 goes into 50 let's add some 0s on the back if I take this decimal move it two to the right take this decimal move it two to the right goes right there so point seven five goes into 50 the same number of times that 75 goes into five thousand so let's do this seventy five goes into 50 zero times seventy five goes into 500 so let me think about that I think it goes into it six times because right because seven times going to be too much so let's go ahead go into it six times six times five is thirty six times seven is 42 plus three is 45 so the remainder is 50 I see a pattern bring down the zero well same thing again 75 goes into 500 six times six times seventy five is going to be 450 again and we're going to keep having that same pattern over and over and over again so it's actually 666 point six six six I hope you don't think I'm an evil person because of this number that happened to show up but anyway so the highest sale price that I can afford or the highest marked price I can afford is \$66 and if I were to round up and sixty-seven cents vote around to the nearest penny if I were to write this kind of as a repeating decimal I could write this as sixty six point six six repeating or I also know that point six six six six going on forever is the same thing as two thirds of 66 and two-thirds but since we're working with money and working at dollars we should just round to the nearest penny so the highest marked price that I can afford is sixty six dollars and 67 cents so if I go and I see a nice pair of shoes for \$55 I can afford it if I see a pair of if I see a nice tie for \$70 I can't afford it with the fifty dollars in my pocket so hopefully this this uh not only will just teach a little bit of math but it'll it'll help you do a little bit of shopping so let me ask you another problem a very interesting problem let's say I start with an arbitrary well let's let's put a fixed number on let's say I start with \$100 and after one year one year it grows by grows by 25% and then the next year year two let's call that year two it shrinks by 25% so this could have happened in the stock market the first year I have a good year my portfolio grows by 25% the second you have a bad year in the 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 sell if I grow by 25% of 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 as I was actually a different amount of money so let's figure this out if I start with \$100 and I grow it by 25% 25% of 100 is \$25 so I grew it by \$25 so I go to 125 dollars right so after one year of growing by 25% I end up with 125 dollars and now this \$125 is going to shrink by 25% so if something shrinks by 25% that means it's just going to be 0.75 or 75% of what it was before right 1 minus 25 percent 75 0.75 times 125 so let's work that out here 125 times 0.75 and it's in case you're confused if something I just I don't want to repeat it too much but if something shrinks by 25% it is now 75% of its original value so if 125 shrinks by 25% it's now 75% of 125 or 0.75 do the math 5 times 5 is 25 2 times 5 is 10 plus 2 is 12 1 times 5 7 ok 7 times 5 is 35 7 times 2 is 14 plus 3 is 17 sorry 7 times 1 is 7 plus 1 is 8 so it's 5/7 and then this is a 7 actually 14 9 94.7 five right two decimal points two decimal points 94.7 5 so it's interesting if I start with \$100 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 hundred 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 hundred and twenty-five that's pretty interesting what you think and that's actually very interesting when a lot of people compare well actually I won't go into stock returns 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 you should think about how much you would have to lose what percentage you would have to lose to end up where you started another interesting project to figure out maybe I'll do that in a in a future presentation but anyway I think you're now ready to do some of that those percent madness problems hope hope you have fun bye