For more information, please see full course syllabus of Basic Math

For more information, please see full course syllabus of Basic Math

### Solving Percent Problems

#### Related Links

- To solve percent problems, translate the sentence into an equation
- “of” means times
- “what” means unknown variable

### Solving Percent Problems

- 50% = .50
- 25 = .50x
- [25/.50] = x

- 20% = .20
- 11 = .20x
- [11/.20] = x

- 40% = .40
- 18 = .40x
- [18/.40] = x

- x ·70 = 35
- x = [35/70]
- x = 0.5

- x ·16 = 4
- x = [4/16]
- x = 0.25

- 15 = x ·1500
- [15/1500] = x
- 0.01 = x

- 30% = .30
- .30(60) = x

- .5x = 15
- x = [15/.5]

- 100% = 1
- 1 ×154 = x

- .25x = 16
- x = [16/.25]

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

### Solving Percent Problems

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

- Intro 0:00
- Solving Percent Problems 0:06
- Translate the Sentence into an Equation
- Extra Example 1: Solving Percent Problems 0:56
- Extra Example 2: Solving Percent Problems 14:49
- Extra Example 3: Solving Percent Problems 23:44

### Basic Math Online Course

### Transcription: Solving Percent Problems

*Welcome back to Educator.com.*0000

*For the next lesson, we are going to go over solving percent problems.*0002

*To solve a problem that involves percents, we want to first translate whatever the sentence is into an equation.*0008

*Whenever you have a number, you are going to write that down in your equation.*0018

*If you have a percent, you need to change it to a decimal.*0022

*You see the word of; that means times; you are going to be multiplying.*0027

*When you see the word what or what number, that means you are going to have a variable.*0032

*That is what you are going to be looking for.*0037

*That is what you are going to be solving for.*0039

*This is almost the same as what we just did the last lesson.*0041

*But now we are going to be looking at variables and solving equations.*0047

*We are going to have to do a little bit deeper into these problems.*0053

*The first set of examples; for example one, 15.*0060

*Remember if we have a number, we are just going to write it straight down into our equation.*0068

*Is; the word is remember means equals; 25 percent; this is write down.*0074

*This we are also going to write straight down.*0083

*But because it is a percent, in our equation, we need to make it into a decimal.*0085

*Percent to decimal, remember we have to move two decimal spaces to the left*0091

*because think of percent as a bigger version of a decimal; decimals are small numbers.*0105

*Whenever you are converting from a percent to a decimal, you have to get smaller.*0112

*The way for you to get smaller is to move the decimal point over to the left.*0118

*The decimal point is over on this side.*0127

*If you don't see a decimal point, it is always at the end of the number.*0130

*We are going to move it one, two spaces.*0134

*The decimal point of 25 percent is going to be 0.25.*0139

*Of course obviously we have to drop the percent sign.*0145

*25 percent is 0.25; that is what I am going to write in my equation.*0148

*0.25; of means times; times what number; this is my variable X.*0154

*Be careful here because whenever you write a dot for times, that looks like the decimal point.*0168

*The best way to represent multiplying is to either write it in parentheses.*0174

*If you are going to show that you are going to be multiplying two numbers, write them in parentheses.*0179

*Or if it is a number with a variable, a letter, then you can just put them together.*0184

*0.25X, that would mean 0.25 times X.*0191

*Here is our equation now; this is what I am solving for.*0198

*15 is 25 percent of what number?--this is the number that I am looking for.*0202

*When I solve for X, remember that since this is 0.25 times X, I need to do the inverse operation.*0207

*0.25 times X, the inverse operation is divide.*0219

*In order to solve for X, I have to divide 0.25.*0224

*0.25 over itself is going to be 1.*0232

*Whatever I do to one side, I have to do to the other side of the equal sign.*0236

*I have to divide this side also by 0.25; this, it looks like a fraction.*0241

*But fractions are division problems; this is the same thing as 15 divided by 0.25.*0247

*Another way to explain why we have to divide, let's say I have 8 equals 4X.*0255

*If I have 4 times a number equals 8, what do I know about X?*0268

*Isn't 4 times 2, 8?--so I know X has to be 2.*0275

*In the same way, I have to solve for X and I can just divide this number by this number.*0285

*Divide this by 4; divide this by 4; 8 divided by 4 is 2.*0292

*That gives me 2 equals X.*0298

*Here 15 divided by 0.25, I need to actually solve that out in order to find X.*0305

*Let's review over how to divide numbers with decimals.*0313

*If I am going to divide these two numbers, remember that the top number is what goes inside when you divide.*0321

*15 on the inside; 0.25 on the outside.*0330

*The decimal point for this number is at the end because we don't see one.*0337

*It is always at the end.*0342

*If I need to add 0s to this number, I can because*0349

*I can always add 0s to the end of a number behind a decimal.*0352

*If it was before the decimal, I can't because then that will just become 150 instead of 15.*0358

*As long as it is behind the decimal and it is at the end of a number,*0364

*you can add as many 0s as you want.*0370

*I can add two 0s; I can add three; I can add ten; however many I need.*0372

*This number, we want to change to a whole number.*0379

*I need to move the decimal point over two spaces to the right to make the decimal point at the end.*0384

*If I move two decimal places for this number, then I have to move this two decimal places over here.*0392

*Then I am going to take that decimal point up.*0399

*25 goes into 15 zero times; 25 goes into 150 how many times?*0403

*Think about quarters; 25 cents or 25 is like a quarter.*0412

*How many of those fit into 100 or a dollar?--four.*0421

*Four quarters is a dollar; think of 150 cents.*0425

*25 cents goes into 150 cents or 1 dollar 50, how many of them?*0428

*That would be six.*0434

*If you want to just check that, this is 12, 13, 14, 15.*0437

*That becomes 0 when you subtract it; I can bring down this 0.*0449

*25 goes into 0 zero times; I have to fill in this space right here.*0454

*That is 0; subtract it; that is nothing.*0461

*I don't have to bring down another 0 because my remainder is 0.*0464

*My answer then, if I do 15 divided by 0.25, is this number up here, 60.*0471

*This number, if there is a 0 in front of the number like that, then that doesn't mean anything either.*0479

*I can just drop the 0; that would just be 60.*0485

*This 0 I cannot drop.*0489

*This 0 has to stay there because if I drop it, my number is going to change to 6.*0491

*We know that 6 is not the same as 60.*0498

*This 0, it is not after the decimal point so we can't drop that 0.*0501

*My answer just becomes 60.*0507

*If you need to review over this, you can either go back to that lesson, dividing decimals.*0513

*Or we are going to do a few more problems that involve dividing decimals.*0520

*The next one, again we are going to change this into an equation.*0527

*1; is is equals; 4 percent.*0535

*4 percent, again we have to change it to a decimal.*0540

*Be careful; 4 percent is not 0.4.*0543

*Again 4 percent to decimal; the decimal point is at the end right here.*0549

*I go one, two; then put the decimal point there.*0556

*I have an empty space that I have to fill.*0561

*I have to fill that with a 0; it is going to be 0.04.*0563

*Again at the end here, one, two, decimal point; 0.04.*0568

*Of means times; blank, that is what we are looking for; that is my variable.*0580

*I am going to put X there.*0589

*Remember if I put number with variable, that means times.*0591

*This represents... I don't have to put a dot here.*0595

*I don't have to use parentheses when it is number with variable.*0597

*Again how do I solve for X?--look at this example again.*0603

*If we are going to do 8 equals 4 times a number, I can take this number, divide it by this number.*0607

*8/4; that is going to give me X.*0614

*Then I have to do this number divided by this number.*0617

*Remember that this over this becomes 1.*0626

*This whole side, my right side, just becomes 1X.*0630

*1X is the same thing as X.*0635

*That is probably a little bit hard to understand, 1X being the same as X.*0639

*But it is like me saying I have an apple.*0645

*If I say I have an apple, you know I only have 1 apple.*0650

*Even though I didn't say I have 1 apple, you just know because how many A's do you see?*0655

*You see one; an A is the same thing as 1A.*0661

*An apple is the same thing as 1 apple.*0667

*Just think of that as having 1X; again we have to divide that; 1.*0672

*Be careful, the top number is going to go inside.*0683

*0.04, the bottom number, is going to go on the outside.*0689

*Again I have to move this decimal point over one, two spaces to the right.*0693

*That means I have to take this decimal point; it is at the end.*0697

*Go one, two spaces; I have to fill these in with 0s.*0702

*There is my new spot for my decimal point; I bring it up.*0709

*4 goes into 10 how many times?--4 times 2 is 8.*0717

*4 times 3 is 12; 12 is too big; it only fits into 10 twice.*0724

*2 times 4 is 8; subtract it; I get 2.*0732

*I am going to bring down this 0.*0738

*4 goes into 20 how many times?--five times.*0741

*4 times 5 is 20; subtract it; I get a remainder of 0.*0746

*I can stop there; my answer becomes 25.*0753

*I don't have to put that decimal because it is a whole number and it is at the end.*0758

*My answer X is 25; right here, this is 25.*0764

*Again 1X is the same thing as X; what did this become?*0773

*This became 25; if 25 is X, then I can just say that X is 25.*0778

*It is the same exact thing.*0786

*The next one, 20 equals 100 percent; to decimal.*0792

*Again start at the end; you are going to go one, two; right there.*0806

*It is going to be after the 1; 1.0.*0810

*Remember if the 0s are at the end of a number behind the decimal point, then I can just drop it.*0814

*Isn't this the same thing as 1?--I can just write 1.*0819

*100 percent as a decimal is 1; times; of means times.*0824

*What number, that is my variable; 1 times X; 20 equals 1X.*0832

*Remember 1X is the same thing as X because if I have 1 apple,*0841

*that is the same thing as just saying I have an apple.*0846

*If you want, you can go ahead and divide the 1 just like we did the other problems.*0850

*20 divided by 1 is 20.*0856

*Whenever you have a number divided by 1, it is always itself.*0860

*20 equals X; or I can flip this around.*0864

*If 20 equals X, then isn't that the same thing as X being 20?*0870

*Either way, that is correct; we just want to know what the number is.*0877

*The number is 20; or you can say 20 is the number.*0881

*It is the same exact thing.*0886

*Let's do a few more examples; these are a little bit different.*0889

*What percent of 50 is 10?*0895

*Now the variable, what we are solving for, is a percent.*0900

*Be careful here; what percent, I am going to make that X.*0907

*Times, times; 50, 50; is, equals; 10, 10; X times 50 equals 10.*0913

*Remember you can change this if you want to 50X just like we did the other problems*0929

*because a number times a variable, you just put it together with the number in front.*0935

*50X equals 10; it is the same thing.*0939

*How do we solve for X then?--how do we get what X is?*0944

*Remember my example?--let's say I have 3 times X equals 6.*0949

*You can do this in your head and know that 3 times 2 equals 6.*0959

*Another way for you to solve it is to do 6 divided by this number; this divided by this.*0964

*Same thing; we can just do 10 divided by 50.*0972

*It is not 50 divided by 10.*0975

*It is this number divided by this number, the one that is multiplied to the variable.*0978

*I can show you this way; 50/50, that is 1.*0985

*10/50, that is what you have to do; 10 divided by 50.*0993

*Again fractions are the same thing as division; 10 divided by 50.*0997

*A shortcut way of doing this is if you are dividing two numbers*1009

*with 0s at the end of it, you can just cross out the 0.*1014

*If there is one 0 up here and one 0 down here, you can just cross out*1020

*one 0 from each of the numbers as long as there is 0s in both numbers.*1022

*But we are just going to go ahead and just divide it this way.*1027

*50 divided by 10; it is not going to go into this number.*1032

*This number is too big to go into this number.*1037

*I am going to have to use my decimal point.*1040

*Do I move it at all?--no, because there is no decimal point here.*1042

*I can just bring it up, bring it straight up.*1047

*I can add 0s at the end behind the decimal at the end of a number.*1050

*Now I can just look at this, 1-0-0, 100.*1057

*50 goes into 100... 50 plus 50 is 100; or 50 times 2 is 100.*1061

*Think of 50 cents; 50 cents goes into 100 cents how many times?*1072

*100 cents is the same thing as a dollar.*1080

*50 cents goes into a dollar twice; this becomes that.*1082

*Subtract it; you get 0; no remainder; that is my answer.*1087

*I don't have to bring down anymore 0s because my remainder became 0.*1092

*When I divided this, my answer became 0.2; X equals 0.2.*1099

*Here is the thing though; they are asking for percent.*1114

*Even though this is my answer, this is my answer as a decimal.*1119

*They want it in percent; they are asking what percent.*1124

*They are not asking what decimal; what percent?*1127

*I have to change this number to a percent; decimal to percent.*1129

*Remember decimal is a small number; percents are larger.*1141

*I have to go from a small to a larger.*1146

*That means I have to move the decimal point over two spaces; but which way?*1148

*If I go to the left, I am going to get smaller.*1154

*But if I go to the right, then I start getting whole numbers.*1158

*I make the number bigger.*1162

*0.2, to make it into a percent, I need to make it bigger.*1165

*I need to go to the right; one, two.*1169

*I have to fill this space with something.*1173

*0.2 as a percent will be 2-0 and then percent.*1177

*The decimal point is right here; it is at the end.*1185

*If it is at the end, remember you can just... it doesn't have to be there.*1187

*You can make it invisible.*1190

*Then we have to write the percent sign because we changed it to a percent.*1193

*My answer is then 20 percent; that is my answer.*1196

*20 percent of 50 is 10.*1204

*Another one; again what percent, make that X, your variable.*1208

*Times 75; is is equals; 7.5.*1214

*Again we have to do this number divided by this number; 7.5 divided by 75.*1224

*Again if you want to see it, I can show you this way.*1235

*because this you have to get rid of by dividing it.*1239

*This 75/75 is 1; X times 1 is just X.*1244

*X equals; then I have to actually divide that to find the answer.*1251

*Here I don't have to move the decimal point anywhere because it is at the end.*1258

*This decimal point will just come straight up.*1263

*75 goes into 75 how many times?--once.*1267

*1 times 75 is 75; subtract it; I get 0.*1274

*I don't have to go any further; 0.1 is my answer; X equals 0.1.*1280

*But again remember it is asking for percent.*1285

*Be careful that you don't forget to change it to a percent.*1288

*I am going to put that here to represent decimal.*1294

*To change it percent, I am going to go one, two, point.*1301

*1; fill this space with a 0; put the percent sign.*1306

*0.1 in decimal becomes 10 percent; X equals 10 percent; there is my answer.*1314

*The last one for this; again what percent X times... of is times... 4 equals 4?*1325

*This one we can just do in our head; what times 4 equals 4?*1340

*Isn't this 1?--1 times 4 equals 4; 4 times 1, it equals itself.*1345

*I don't even have to solve this; I can just make X equal to 1.*1352

*If the problem is fairly easy, you can just do it in your head, then go ahead.*1356

*There is no need for you to do all the work unless your teacher wants you to show the work.*1360

*Then X equals 1; since X equals 1... I didn't mean to box this.*1367

*That is not my final answer so I don't want to box it.*1381

*Since X equals 1, I need to change it to percent.*1385

*How do you change a 1, a whole number, into a percent?*1391

*Again where is the decimal point?--I don't see it.*1395

*If I don't see it, it is invisible, it is at the end like that.*1399

*Go one, two, point here; I have two spaces to fill.*1404

*This becomes 1-0-0 percent; this X equals 100 percent.*1411

*The next example, we are just going to do a few more, just different types though.*1428

*The other examples, they were the same kind, all the problems on that page.*1433

*15 equals what percent, X, times 150; let me rewrite this equation out.*1439

*Since this is 150 times X, let me just write it here.*1452

*15 equals... remember whenever I do a variable times a number,*1458

*I want to write it together but with the number in front; 150X, like that.*1463

*Then to solve for X, remember I have to do this number divided by this number.*1471

*I am going to divide this side by 150.*1478

*Whatever I do to one side, I have to do to the other side.*1480

*That way this becomes 1X or 1 times X; 1X.*1486

*That is the same thing as X.*1492

*15 divided by 150; no decimal point here; I don't have to move it.*1495

*Instead I need to draw that in; bring it up; add 0s.*1509

*150, we know it doesn't go into 15.*1518

*If you want, you can put a 0 up here; if not, then that is fine.*1523

*Just remember that it is now the next three or just these three.*1525

*150 goes into 150 one time; that becomes 150.*1530

*If you subtract it, it becomes 0; I drew an extra 0 there.*1536

*But you don't even have to bring it down because it is just going to be 0s.*1542

*Remember 0s at the end of a number behind the decimal point means nothing.*1545

*0.1 is my answer; X is going to equal 0.1.*1551

*You can also say 0.1 is going to equal 1X or X; same thing.*1558

*But I can switch it like this; it is asking for percent.*1564

*I need to take this decimal point and go one, two; fill in this space.*1572

*It is going to be 1-0 percent; 0.1 is the same thing as 10 percent.*1579

*The next one, 30 percent, this is written out as percent.*1592

*But it still means the same thing as percent like that.*1599

*30 percent, I have to change that to a decimal.*1602

*30 percent becomes... at the end, you go one, two, right there.*1606

*0.30 or 0.3 because remember it is 0s at the end behind the decimal.*1613

*It doesn't mean anything.*1619

*0.3 or 0.30; of, times; 12; it is number times number.*1621

*I can't write it next to each other like how I do numbers with letters.*1629

*I have to put it in parentheses.*1633

*Is is equals; what number, this is my variable.*1637

*All I have to do to figure out what X is is multiply those two numbers.*1645

*0.30, you know what?--we know that the 0 means nothing.*1654

*Let's just make it easier and just not even have that 0.*1660

*One digit number is easier to multiply.*1665

*I am going to put the 12 on the top; 0.3 on the bottom.*1669

*Multiply it; 2 times 3 is 6; 3 times 1 is 3.*1673

*From here, I only have one number behind the decimal point.*1680

*Start at the end; go place the decimal in there.*1685

*What I just did, when you multiply decimals, you have to count...*1692

*This decimal point is at the end, right here.*1695

*You count to see how many numbers are behind the decimal point.*1698

*Here I only have one; then I start at the end.*1702

*I only go one inwards; that is where the decimal place goes.*1705

*X is 3.6; to finish this equation, 3.6 equals X.*1711

*3.6 is the number; or I can say the number is 3.6.*1723

*The next one, 5 percent, change that to a decimal.*1734

*Start here; go one, two; it is point... fill in that space.*1741

*It is 0.05; it is not 0.5; 0.05.*1745

*0.05 times my unknown which is X; X equals 4.*1752

*Again I have to solve for X which means I have to divide.*1764

*4 divided by 0.05; 4 divided by 0.05.*1768

*I have a decimal point here; I have to move it one, two.*1779

*There is my decimal point; I am going to move it one, two.*1784

*Bring it up; fill in these spaces with 0s; 5 goes into 4 zero times.*1788

*5 goes into 40... 5 times we know 8 is 40.*1797

*Write 40 down here; subtract it; 0.*1804

*I am not finished with the number yet because I still have space up here.*1808

*Bring down the 0; 5 goes into 0 zero times.*1814

*That is why for this, I have to keep going.*1818

*Even though this became a 0, I have to bring down the 0 and solve it again*1820

*because there was an empty space before my decimal point.*1826

*In that case, you have to continue.*1831

*If it is after the 0 like in this problem right here... I'm sorry.*1833

*If it is after the decimal point, then I can stop once I get 0 as my remainder.*1838

*But for this, if there is a space here before the decimal point,*1844

*then I have to go again until I fill in those spaces.*1849

*Here this is 80; X is 80; they are not asking for percent.*1852

*5 percent of 80 is 4.*1861

*The last one, 100 percent of 3448 is what number?*1866

*They are asking for 100 percent of this number.*1874

*100 percent is all of it, is the whole thing.*1877

*100 percent of this number is just this number.*1883

*If you want to solve it out how we solved out the rest of them,*1888

*100 percent as a decimal, again move the decimal point over one, two spaces.*1891

*That becomes 1 or 1.0 which is the same thing as 1.*1898

*Times; times 3448; I am going to change this to parentheses.*1905

*3448 equals what number?--X; 1 times this number is just that number.*1912

*I can say 3448 is the number or the number is 3448.*1926

*That is it for this lesson; thank you for watching Educator.com.*1948

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