 This video will be on percents. When you look at percents, when it says 10%, that means that it's 10 out of every 100. Or in a fraction form, we could put 10 over 100, which would reduce to 1 over 10, which looks like 0.1. Okay, so if you look at 10 and you want to think about the decimal, 10% would be move the decimal two places to the right, and it's equal to 0.1. If I have 3%, I'm going to move the decimal two places to the right, 1, 2, and I'm going to have 0.03. So it asks us for a Michigan sales tag of 6% of its items price. So let X be the cost of an item. First it wants us to find the sales tax. So we take 6% or 0.06 times the price is really what we're doing. So we're going to have 0.06X. That would be our tax. Now it says find the total cost. Well, total cost is going to be the price plus the tax. Well, we already know that the cost, maybe I should be putting costs in here. Our cost is the same thing as price. This would be easier to fix. So prices X plus our tax that we just found to be 0.06X. And if I combine those, I'd have 1 plus 0.06 times X or 1.06X. So let's get into a little bit more involved problem. Ian puts 10% of his monthly income in a savings account. He makes $500 each month. How much does he put in his account each month? Well, remember that we want 10% of his monthly income of his monthly income. So 10% times and his monthly income is $500. So we would translate that to 10% or 0.1. So we can put it in our calculator times 500 and that would be 50. He puts $50 in each month. After a little bit, he'd have a nice chunk of savings. All right, so Ethan puts $4,000 in a CD earning 6% annual interest and a savings account that earns or pays 3% annual interest. And he puts the 4,000, that's the total that he puts in. Okay, if Ethan earns $210 in interest from two accounts in one year, how much did he invest in each account? So he earns 210. So let's put this into perspective. What he earns is made up of the amount that he invests times the 6% the amount at 6% times that 6% plus the amount at 3% times the 3%. Now we have to do a little bit of fancy thinking here. All we know is that the total is 4,000. But if he puts X dollars in the 6%, and he has a total of, when I add them, I'm going to have 4,000 here. Well, if you start with 4,000 and you take off X, when I say you take off X or take out X to invest, what do you have left? You have 4,000 minus X. You subtracted the X amount, and that's how much he's going to invest at 3%. So he earns, go back up, he earns 210. And that's going to be equal to 6% or .06 times the amount he invested, which we decided over here was X, plus the amount that, or 3%, the decimal going first is usually nice, times the amount he put in there, and we decided that that was 4,000 minus X. Okay, we have decimals, so we need to clear them. It's going to make for big numbers, but pull your calculator out. So if we're going to do that, we have to multiply everything by, we've got two decimal places, so we're going to multiply everything by 100. So 210 times 100 is going to be 21,000. We've got three zeroes. And 100 times .06 times X is going to be, I'm going to go ahead and put that back in green. That's going to be 6 times X. And then plus 100 times our .03 times our 4,000 minus X. And that gives me plus 3, 100 times .03. And I still have to distribute that to the 4,000 minus X, because remember we can only multiply two things at a time. So 21,000 is equal to, and 6X is just 6X. There's nothing I can do there. But then 3 times 4,000 is going to be 12,000. And 3 times negative X is going to be minus 3X. So on this side, I'm going to have 6X minus 3X, or 3X plus 12,000. And on the other side, I'm going to have my 21,000. And so I need to subtract my 12,000 from both sides. That's going to give me 9,000 equal to 3X. And when I divide by 3, then X is going to be equal to 3,000. Now it said, I'll make sure you answer the question, how much did he invest in each account? So he invested $3,000 at X, which was at 6%. But how do I know how much he invested at 3%? Well, 4,000 minus 3,000 here is going to be $1,000. And $1,000 at 3%. He invested 3,000 at 6% and 1,000 at 3%. Remember, we always answer in a sentence. Emma receives a 2% raise at work. If she makes $1560 per hour now, and she had a 2% raise, we want to know what her rate was before her raise. So we need to know X is going to be her rate before the raise. I know if we have a rate before plus the 2% of that rate, that will give us her final of $15.60. So we have X dollars that she started out with plus converting .02 times that X dollars should be equal to 1560. Well, we have wonderful decimals here, so we have to multiply by 100. And you'd have 100X plus distributing over here, you'd have 2X and distributing all the way over here is equal to 1560. So 102X is equal to 1560. And when we divide by 102, we find out that her original rate was 15.29. It's actually 15.294. But since we're talking about dollars and cents, I'm going to say that she made $15.29 per hour before the raise. I know that somebody's going to ask me, did we have to clear the decimal? At this point right here, we could have said that that is 1 plus .02 times the X is equal to the 15.60, which is really 1.02X equal to 15.60. Yes, you could have used decimals if you're using your calculator anyway. You would divide by 1.02 and divide this side by 1.02. And X is again equal to that 15.294, which we say is approximately 15.29.