Suppose I go to the store and I have $ 50 in my pocket. $ 50 in my money box. And the day I go to the store, I learn that There is a 25% discount on selling prices. 25% discount means that the current price If it’s $ 100, I’ll pay It will be 25% less than 100. But if I have $ 50, that’s the maximum current price I can afford what will it be equal to? We need to be able to see what we will get next we can decide. Now let’s do a little algebra. Suppose x is the maximum price I can pay. If the selling price is 25% less than x, then the new price, that is, the selling price will be equal to “x minus 25% x”. And suppose there is no sales tax in the country where I live. Whatever the selling price, I have to pay it in cash. Thus, “x minus 25% x” is equal to the selling price. The discount is 25% of x. But we know that we can also write the equation as “x minus 0.25x”. And we know that in our equation our x is equal to 1x. 1x minus 0.25x This means that the selling price is 0.75x. We first rewrote “x minus 25% x” in the form “1x minus 0.25x”. and we got 0.75x. Because when you subtract 0.25 from 1, you get 0.75. So 0.75x is our selling price. So what is the selling price I can afford? The selling price I can handle is $ 50. In that case, 0.75x equals $ 50. If x is greater than the number we are looking for, The selling price will be over 50 and I do I will not be able to meet. Therefore, we determine in advance the maximum price we can pay – $ 50 and this is our selling price. To solve our equation as before, you just need to divide both sides by 0.75. And the maximum price we can pay It is equal to the ratio of $ 50 to 0.75. Let’s calculate this number. To find out how many 0.75’s are in 50, let’s increase the number of 0s after 50. If we move this decimal to the right by 2 units. We also need to move this decimal by 2 units to the right. Thus, the number of 0.75s in 50 It is equal to the number of 75s in 5,000. Let’s solve now. 50 does not contain 75. But we can divide it because it is within 75, 500. I think there are six 75s out of 500. Because 75 times larger numbers are taken 7 times. So 6 times 75 gives us less than 500 numbers. The product of 6 and 5 is equal to 30. 6 times 7 gives us 42. plus 3 is equal to 45. Thus, the remainder 50 is obtained. We bring down 0 and the same calculation again. The number of 75 out of 500 is equal to 6. 6 times 75 gives us 450. Again, the remaining 50 is taken and the same operation we have to do it several times. Our answer is 66,666. I hope because of the consecutive 6s You don’t think I’m the devil. In any case, the maximum selling price we can pay, or in other words, the maximum current price is $ 66. But if we have to round our cents, We would have received 67 cents. If we do not round, we can write our answer as 66.666 …. or, we know that 0.6666 … numerical Is equal to the ratio of 2 to 3. Thus, our answer can be written as 2 out of 3 in 66. But because our operation is about money we can’t write our cents in 2/3 form. Therefore, the maximum price we can pay is $ 66.67. So if we come across a nice pair of shoes for $ 55 in a store, we can easily get it. But if we see a beautiful tie for $ 70, we can’t get it for $ 50 in our pocket. I hope this is not just for you to learn algebra, will also help you shop. Let me ask you another question, very interesting issue … Let’s say we start with a certain number. For example, I’ll start with $ 100. And a year later our amount increases by 25%. Next year, in our second year our amount is starting to decrease by 25%. Such cases occur in the stock market. The first year is successful and our portfolio Increases by 25%. The second year does not bring us luck and our portfolio is reduced by 25%. My question is that at the end of two years we how much money will we have? Many people may think that this is too easy. If first our money increases by 25% and then decreases by 25%, we will have the same money at the end of two years. But I’ll show you that it’s not as simple as you think. Because 25% change in different years equal to different amounts of money. Let’s calculate. We start with $ 100, and in our first year there is a 25% increase, and 25% of 100 is equal to 25. That’s an increase of $ 25. Thus, at the end of the first year, the amount is $ 125. That is, after a 25% increase in our first year, we end that year with $ 125. Now that $ 125 is starting to fall by 25%. If the price of something decreases by 25%, it means that the answer received is equal to 75% of the previous price. 1 minus 25%. 0.75 times $ 125. Let’s calculate here. A product of $ 125 to 0.75. You can only be confused at one point, which I don’t want to repeat too much – a 25% reduction in something is equal to 75% of it. Thus, a 25% reduction of $ 125 equals 75% of $ 125. Let’s solve now. 5 times 5 is equal to 25. 2 times 5 is equal to 10, plus 2 is equal to 12. 7 times 5 is equal to 35. 7 times 2 is equal to 14. Plus 3 is 17. Sorry. 7 times 1 is equal to 7. Plus 1 is 8. And because when you add 5, 7 and it’s scratch-black 7 14 9 94.75. Two decimal places 94.75. It’s very interesting. If I start with $ 100 and that amount increases by 25%, then if it decreases by 25%, I have less than the amount I started. And I want you to understand that The amount of a 25% increase of $ 100, ie $ 25 25% is less than the amount we lost, ie 75% of 125. I’m losing 25% of $ 125. That’s very interesting, isn’t it? Because many people compare numbers tries to do … stock earnings and so on. about I do not want to talk. However, operations with numbers are quite interesting. You should get acquainted with other examples. Another interesting issue is the time of earning a certain interest you have to think about how much you will lose. That’s a percentage loss compared to the number you started you will face. This is another interesting issue. Maybe I’ll do it in one of the future presentations. Anyway, I think you already have some you are not ready to solve interest problems. I hope you have fun. Thank you.

Algebra