Percent word problems: tax and discount

we're told that Casey buys a bracelet she pays for the bracelet and pays 72 cents in sales tax the sales tax rate is 6% what is the original price of the blade bracelet before tax so pause this video and see if you can figure this out well let's think about how your sales tax is calculated your sales tax sales tax would be equal to the sales tax rate I'll just call that the rate so that's going to be equal to the rate times your original price original original price and what do we know here well they tell us what our sales tax is our sales tax is 72 cents so I'll write that here so 72 cents is going to be equal to my sales tax rate they also tell us that that is 6% it's going to be equal to 6% times my original price and that's what they're asking for the original price so times I'll just call it let's just call it P for short original price and so you have it we have a fairly straightforward equation now and now I'm just going to rewrite everything as a decimal so we could write we could write 0.72 is equal to 6% is the same thing as 6 per hundred which is the same thing as 6 hundredths 0.06 6 hundredths times P and now we can just divide both sides by 6 hundredths to solve for the original price so let's do that all right so on the right hand side I have a P on the left hand side if I have 72 hundredths divided by 6 hundredths well that's going to be equal to 12 12 times 6 is 72 6 hundredths times 12 would be 72 hundredths and so this is going to be equal to is going to be equal to 12 so the original price of the bracelet before tax is $12 and you can verify that 6% of $12 zero point zero point zero six times 12 is indeed seventy-two hundredths let's do another example a store has a 25 percent off sale on coats with this discount the price of one coat is 34 50 what is the original price of the coat so once again pause this video and see if you can figure it out and this these examples they're actually quite useful because you will encounter this all of the time when you are shopping or you're trying to calculate tax or you're buying something so think about this can you figure out the original price of the coat all right well let's just write out write it out the same way we did last time so let's say original price original price and then there's a 25% discount so minus 25% of the original price original original price is going to be equal to 34 50 is equal to 34 50 because that's the price with the discount so can we solve for the original price so one way to think about it this is 100 percent of the original price or one times the original price minus 25% of the original price is going to be equal to this well 100% minus 25% of something is going to be 75% of our original price original this is why people use letters for variables so they don't have to keep writing this over and over again is going to be equal to 34 50 and now to solve for our original price we just divide both sides by 75% and 75% that's the same thing as 75 per hundred or 75 hundredths so I could divide both sides by 75 hundredths 75 hundreds on the left-hand side these two are equivalent so I'll be left with my original price and now I just have to figure out what is this going to be so if I take 75 hundredths and let me actually multiply both of these times 100 so this is going to be the same thing as three thousand four hundred and fifty divided by 75 I just did that to get rid of the decimals I moved that essentially the deaths of both decimals to the right two places multiplying the numerator and the denominator by 100 so let's see how many times seventy five goes into three thousand four hundred and fifty see seventy-five doesn't go into three doesn't go into 34 it does go into three hundred forty-five what is that four times four times five is twenty four times seven is 28 plus two 300 and then you subtract you have 45 bring down the zero 450 seventy five goes into 450 six times six times five is thirty six times seven is 42 plus three is indeed 45 and we luckily have no remainder so this right over here is going to be equal to forty six dollars our original price is forty six you take off 1/4 or 25% you're left with thirty four fifty and that makes intuitive sense as well always good to just take whatever answer you have and put it back in and see if if it makes sense in terms of you know somehow you got four hundred sixty dollars they said taking 25% off you get to thirty four fifty you said well that sounds off or if you've got four dollars he said you take 25% off and you got thirty four fifty that would have also felt off but forty six dollars feels right and you could even calculate that what is 25% of forty six dollars subtract that from forty six and you should get $34.50