SABIS G6 Math CP 5.3

Added: 2026-05-07

[00:00:00]Section 5.3 is talking about percentages. Question one, this is the hardest question that you may get. I will show you an easy way to do it. He's telling you that 55% of employees in a company drive to work. He didn't tell you how many employees. So this is the company. This is the total number of employees in the company. 55% drives to work. Come on. The other don't drive, which is 45%.

[00:00:28]30% of the employees who drives to work are women. So this is who drive. 30% of these who drives are women. So this is the number of women. The one the other would be the number of men.

[00:00:45]He told you that there are 99 women working in the company. So here you have 99 women. What does he want? He want how many employees drive? He wants this. And then how many employees in the company?

[00:00:56]If he told you 5% of 10, what do you do? You do 5 over 100 * 10 and you get it the 5% of 10, which is 0.5.

[00:01:09]If he told you 5% of what number is 10 here, what do you do? You don't know this number. So you say 5 over 100 of this number, which I don't know is equal to 10. And what do you do? You you multiply here by 100 over 5 and here by 100 over 5. This will totally cancel this and here you will simplify divided by 51 by 52. So this is 200. So what did you do? If you told you 5% of what? He didn't give you the gross number. He gave you the small percentage. What do you do? You just flip this and multiply it here. This is exactly what I'm going to do. I'm going backwards from the small to the big. So what I will do I have to flip the percentage that he gave me. So to get the number of people who drive 99 * I will flip this 30 over 100 will go with the 0 divided by 31 by 3 33 33 * 10 3 0 employees drive to the company. So this number is 330.

[00:02:19]Same way here I'm going from the small to the big. So I will flip this 330 * 55 over 100 and then simplify divided by 11 is 5 divided by 11 is 3 and the 0 is still here by 5 is 1 by 5 is 20 0 0 2 * 3 is 6. So total number of employees in the company is 600. So, if you have the small and you need the big, you will flip the percentage. If you have the big and you need the small, you will keep the percentage the same. Here, I'm going backwards. It gives you the small number and he wants the question two. A basketball player threw a total of 40 free throws during a certain season. The player made 35% of the shoots. So, total he make 40 shoots.

[00:03:13]How many scored a goal? 35%.

[00:03:19]The number of shots he made was how many shots and then the number of shots he missed. So he wants how many one he scored and how many one he didn't score.

[00:03:29]Tabby told you that he scored 35%. So 35 over 100 of total 40 he did. 0 will go with the zero uh divided by two is equal to 5 divided by two is two by five 1 by 5 7 7 * 2 is 14 so he scored 14 goals out of the 40 shoots he made how many he missed you can say 14 - 14 * 4 is 6 3 * 1 is 2 so he made 26 he missed 26 and he scored 14 in simplest form he wants the ratio of the shoots he made to the he missed. So the ratio is 14 to 26 in simplest form divided by 2 is 7 divided by 2 is 13. So in simplest form 7 to 30. If you want to check your answer in a question like this you know that he made 35%.

[00:04:30]So what he missed is what? 100 minus 35.

[00:04:33]So what he missed is 65. If you simplify 35 / 5 is 7, 65 / 5 is 13. You'll get the same answer. And if there is no time in the exam, don't don't check your answer.

[00:04:49]Question three.

[00:04:51]And if there is time in the exam, please check your answer. Question three. Logan bought a keyboard initially priced at 50. So the initial price is $50.

[00:05:04]The keyboard was put on sale for $30.

[00:05:06]So, it was put on sale for $30.

[00:05:11]What is the He wants the percentage of the original price.

[00:05:16]What percent of the original price was the discount? How much was the discount?

[00:05:19]He bought it for 30.

[00:05:22]And the initial price is 50. Here he wants the percentage. So, the final price over the initial price.

[00:05:29]So it is 3 to 5 multiply by two it is 6 over 10. So it is 60 over 100. So 60% he paid. So uh 40% is the discount. If you're going to forget to make 100 minus 60 is equal to 40 and you only want to get the discount. So how much money was discounted? He paid 30. The total price is 50. So the discounted price is 50 minus 30 which is 20. So this is the discount.

[00:06:06]And be careful here. He wants the percentage of this discount which is 20 over 50. If you multiply by 2 it's 40 over 100. So it's 40% discount.

[00:06:18]How much he paid? 60%. Which is 30 over 50. How much is the discount? 40%.

[00:06:25]which is what he didn't pay over the original price. So please don't get confused if he want the discount.

[00:06:33]It's the original price minus what he paid over the original or you get the the what he paid divided by the original you will get what he paid is 60%. So how much is the discount? 100 minus 60. So the discount is 40.

[00:06:54]Question four. Harvey bought shoes initially priced as at $200. So 200 is the initial price. They were put on a sale for 100. So he paid 100. 100 is half the 200. The amount of discount, how much is the amount of discount? 200 minus 100 is 100.

[00:07:14]Which is how many percentage of the original priced amount? This is easy.

[00:07:18]100 over 200 is one over two. So the discount is 50%.

[00:07:25]This is very easy. 45% of 400. So 45% is 45 over 100 * 400. 0 0 0. So 4 * 45. 4 * 5 is 20.

[00:07:37]44 16 + 2 18. So 118.

[00:07:42]What is 07 as a percentage? As a to get this as a percentage you will multiply by 100. Same like when you transfer the percentage to a number you divide by 100. So here this is times 100. So the decimal will shift by two 1 2. So this is 7.5%.

[00:08:04]80% of 150. 80% which is 80 over 100 of 150. 0 goes with the zero.

[00:08:13]10 / 5 is 2. 15 / 5 is 3 / 2. 1 / 240. 0 goes down. 3 * 4 is 120. So 80% of 150 is 120.

[00:08:29]Number eight. In a flower shop there are 150 flower. 20%. Okay. Here I have total 150 flowers. Here he give you the number 1 5 0. He give you the total number.

[00:08:41]Okay. Not like the first question. He didn't give you the number of employees.

[00:08:44]20% of these flowers are roses. So here, how much are the roses? 20%.

[00:08:56]Fill in the blank. The number of flowers that are not roses, how how many are roses? 150 * 20 over 100. 0 goes with the zero. 0 goes with the zero. 2 * 15 30. So 30 is roses. How many not roses?

[00:09:13]150 - 30 uh 150 - 30 is 120. To check your answer, if 20% are roses, 80% are not roses. So, let's try 150 * 80 over 100.

[00:09:28]0 0 0.

[00:09:31]8 * 5 40 0 down 4. 8 * 1 is 8. 8 + 4 is 12. So, I have 120 that are not roses.

[00:09:40]The ratio of roses to other flowers it is 20 to 80 2 to 8 is exactly 1 to4 or 30 to 120 again 30 to 120 will go with the 0 divided by 3 1 / 3 4 again it is 1 2 4 so if you compare roses to roses or percentage to percentage you'll get the same it is 1 2 4 question nine what percentage of 140 is 56. So he wants 56 is how many percentage of the 140? So 56 over uh 140. Let's simplify first. Divided by 2 is equal to 70.

[00:10:22]Uh or I can just divide by 7. Actually divided by 7 uh is equal to 20 divided by 7 is equal to 8. So 8 over 20. I want the denominator to be 100. So I multiply by five.

[00:10:38]So this is 100 8 * 5 is 40. So this is 40%.

[00:10:46]Which is b 40% of x is 60. As I said 40% which is 40 over 100 of x is equal to 60. So here you flip you flip and you if you're going to multiply by the small one you flip it. So times 100 over 40 * 100 over 40 or you just multiply flip this and multiply it here. So the zero will go with the zero. 6 * 100 is 6.

[00:11:15]Uh sorry here 0 goes with the 0 divided by 2 is uh is divided by 4 is equal to 1 divided by 4 is 25. 25 * 6 6 * 5 is 0.

[00:11:29]Zero down, three up. 6 * 2 is 12. 12 + 3 is 15. So the answer is 150.

[00:11:40]11. Part A. 30% of X is 39. What is X?

[00:11:45]So here I will flip 39* 30%. 30 over 100.

[00:11:53]0 will go with the zero. 3 / 3 is 1 / 3 is 13. So 1 3 0 here this one. Part B. What percent of 150 is 60? So he needs to know 60 is what percentage of 150? 60 over 150 0 by 3 2 by 3 5. You can just multiply by uh by um by 20 by 20.

[00:12:30]So 5 * 20 is 100. 2 * 20 is 40. So it's 40%.

[00:12:37]Mara has 135 scarfves in her collection.

[00:12:40]So she has a total of 135.

[00:12:45]40% of the scarfves are made of silk. So 40% is silk.

[00:12:54]How many scarves are not made of silk?

[00:12:57]How many are not made of silk?

[00:13:00]not silk. If this is 40, so this is 60.

[00:13:03]So you can say 60% which is 60 over 100 times 135.

[00:13:11]0 goes to 0. 10 / 5 is 2. Uh 13 and 6 sorry 135 / 5. I'll do it here. 135 / 5.

[00:13:23]This is uh 2. 2 * 5 is 10. 35 / 5 is 7.

[00:13:29]So this is 27 divided by 2 1 / 2 3 3 * 27 3 * 7 21 3 * 2 is 6 + 2 8. So this is 81.

[00:13:44]You want to check your answer. 135. What is 40% of 135? I'll do it here. 40% of 14 35 40 over 100 * 135 0 0 5 2 5 I just did it 27 2 1 2 2 * 27 2 7 is 14 2 * 2 is 4 + 1 5 so this is 54 you want to check your answer 8 1 + 4 is 5 8 + 5 is 13. So my answer is correct. So what is not silk is 81.

[00:14:26]If in simplest form the ratio of the scarf which is made of silk that is 40%.

[00:14:33]2 what is not made of silk 60 100 - 40.

[00:14:36]So it is 4 to 6. 4 to 6 again divide by two it is 2 to three. So this is 2 to three. That one is easier than making 54 to 81. and then simplify again it will come 2 to three. Question 13. Uh given that 15% of x is 60 what is x? Again I will flip this. So 60 * 15 over 100 over 15 because I flipped it.

[00:15:05]Uh 15 / 5 is 3. This is divided by 5 is 20 divided by 3 1 / 3 is 20. So 022 is four. So answer 400.

[00:15:22]If 15% if 15 is x percentage of 50 and here you want the percentage. So 15 over 50 just multiply by two up and down 30 over 100.

[00:15:36]So it is 30%.