Solving Word Problems Involving Numbers - Algebra Word Problems

In this lesson, we will learn how to solve algebra word problems involving numbers.

Hi, welcome to the Algebra Word Problems Tutor and in this class I am very excited about teaching this class because up until now my other courses and in your school work you have learned how to do algebra. You have learned the mechanics of how to do algebra. You have learned how to solve an equation, had a add negative numbers and positive numbers in things like that and then given a problem, you have the tools in your toolbox to try to be able to solve that kind of problem but everybody knows that in the real world and also in your test you are going to be given a certain kind of problem called the word problem and that makes people sometimes have a hard time and the reasons is because your problem is not given to you in a nice one line fashion and it does not just say solve this equation or manipulate this expression. The word problem has a challenge to it because it is bunch of words and use numbers in there and Sally and Jane and different peoples names and so on. And you are challenge really with those kinds of problems because you have to take the information out of the problem and put it on your board or on your paper. And then trying to get to the math usually is not that hard. Trying to get through the math usually is not that difficult the actual solving of the problem. The real challenge with the word problem is actually taking the information out of the problem and constructing to your equations or whatever it is you are trying to do on your paper. That is the real challenge and to be honest with you that is real life. Your real life is not giving you a bunch of one liner homework problems real life is go figure out how to make this airplane fly or go figure out how this engine is running to hot, go figure out why it is running to hot and fix it. So what are we going to do in this course is this course is going to be 100% word problems. That is all it is. The actual math behind it, the actual solving the equation is not going to be that hard and I did that on purpose. The challenge is taking the word problems and taking that information out and putting it into a problem form so you can solve it. That is what we are going do today. So the first section is Algebra word problems involving number. Basically these problems are going to have one number relating to another number sometimes its age, sometime its distance things like that, and I think the word problems just like anything else in life the easiest way to learn how to do them is just to see some examples so let us go and find those examples. The first problem that we are going to do and talk about is on your board here and it says on your screen right here and it says, four times a number increase by two is equal to 30. What is the number? The number one thing in you need to do when you are solving word problems any kind of problem that has a sentence involved in it is called a word problem is you have to understand what is actually asking you. Number one thing people do is you see a word problem and people start trying to write down answers and numbers and equations without actually understanding what the problem is saying and what is asking you. You have to do that so do not try to skip ahead. Read this problem two or three times until you understand what is actually asking you to do then start writing down your equations and your numbers and so on. So let us read it one more time. Four times a number increase by two is equal to 30. What is that number? So we have a number that is what we are trying to find and we multiply it times four and then we take that thing and then we add two to it and then the resulting answers should be equal to 30 and what we are trying to do is try to find that number. So what we are going to do because we have an unknown here, we have a number okay we are going to say that the variable x is equal to the number. The reason I am doing this is because I really do not know what the number is that is the whole point, I do not know what the number is so I am going to assign a variable to it. And remember way back to being in algebra that is what are you doing here you do not know what it is. So it is a variable, it is the unknown. So you assign it to be x. So what you want to do is you want to translate this problem into an equation or something you can solve. So four times a number increased by two. Well if my number is what I am trying to solve for, then four times a number must be 4x four times a number. Increase by two then I am going to add two to it. It has got to be equal to 30. Congratulations you have just translated your first word problem into an equation. Four times a number increase by two is equal to 30 and now what we have to do is solve for our unknown. So to do that, going back to your basic algebra we will subtract two from both sides so this two will go away two minus two is zero and on the right side we will have 30 minus two. So all have I done is to subtract two from the left and get rid of that two and two from the right, I actually have not done any math yet so 4x is equal to 28 and then into it you solve for x. You divide both sides by four so x is going to equal to 28 divided by four so on the left 4x divided by four will give you one so that is why you have one x there and 28 divided by four. So x is going to be equal to seven. X is going to be equal to seven. So you see what you did here is you had a word problem that you translated into an equation 4x+2=30 and you just use your math to solve that equation and here is your answer. Now the great thing about word problem, actually the great thing about algebra in general but especially word problems is a you know you can always check your work always 100% almost always you can check your work and you should do that with every problem and it is really easy to do because now you that figured out what number is which we said in now it is equal to seven you want to see if that is the right answer. So that is the great thing when you are taking a test you will always know if it is right. So do not pass up the opportunity to figure out if you did the right thing. So now if your number is equal to seven which is what we said let us just read the problem one more time. Four times a number four times a number see now we figured out what this number is let us put in here four times a number increased by two, this has got to be equal to 30. Well, let us see what it is equal to seven times four is 28 plus two; we will just keep that there because we have not done anything yet. 28 plus two is equal to 30 okay. We have done the right thing. We know we have done the right thing because we done our math, we found our number, and then when we apply the logic back to our number that we found, we get exactly what we should get. The second problem is a little bit more complicated but not too much more complicated we are just going to build in complexity here. Second problem the sum of two numbers is 30 and one number is two times the other number. What are the two numbers or find the two numbers so again same thing as before you have to read the problem, understand the problem, and then start writing stuff on the paper, okay. The sum of two numbers now remember the word sum, the word sum is adding two things together. The sum of two numbers is 30 and one number is two times the other number. Find the numbers. So let us go ahead and just tackle this one step at time. Now we have two numbers. We all have one number, we have two numbers and you can tell because the problem might there says we have two numbers so you know this so we can say that a variable x is equal to number one and the variable y is equal to number two. Now in this problem we know we have to have two numbers because it says right here in the very first sentence the sum of two numbers is 30. So you know and you are trying to find the two numbers you know you are going to have two variables and that what tells you, you want to have two variables right there. So let us go ahead and translate that first sentence. The sum of the two numbers x+y that is the sum of these two numbers that we are trying to find is 30. So we have already translate