Solving Word Problems- Steps & Examples

دوره: GRE Test- Practice & Study Guide / فصل: GRE Quantitative Reasoning- Numbers and Operations / درس 3

GRE Test- Practice & Study Guide

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Solving Word Problems- Steps & Examples

توضیح مختصر

Watch this video lesson to learn how you can solve word problems by following this 3-step process. Learn how to visualize your problem so you fully understand it. Then learn how to write and solve your equations.

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Our Word Problem

Yes, this video lesson is about word problems . I know for many, word problems are considered a nightmare. But they don’t have to be confusing. Let me show you a 3-step process you can use to help you solve your word problems. You will need your algebra skills for solving equations with variables in them, so access that part of your brain right now so that you have that information at your disposal during this video lesson.

We begin with a word problem.

Tobias is scared that the banks will close on him, and he’s afraid that a fire will come and burn everything he has. So, he keeps his cash savings frozen in a big piece of ice in the freezer. He has $4,300 in frozen cash. His brother, Jude, keeps his cash stuffed inside a teddy bear. Jude has half the amount that Tobias has. How much money does Jude have stuffed in his teddy bear?

Step 1: Visualize the Problem

The first step is to visualize the problem. See if you can picture what is going on. Draw pictures if that will help you. Pinpoint or highlight the important parts of the problem.

For our word problem, we can picture two brothers with cash savings. We can picture Tobias opening his freezer to look at his cash. We highlight the important part of how much cash Tobias has. We do the same for Jude. We picture Jude giving his teddy bear a hug. We highlight the important part on the amount of cash Jude has in his teddy bear.

But wait. We don’t know how much Jude has. That’s the amount we want to find out. So, we label it with an x and highlight it. We might make a note next to the x that this is what we want to find out. We also understand from the problem that Jude’s amount is half of the amount of Tobias. We write that information next to the x . We can write x = half of Tobias’ amount.

Step 2: Write Your Equations

Now that we fully understand the problem, we proceed to step two, which is writing our equations. From our visualization of the problem and by highlighting the important parts, we have already begun to write our equation. We only need one equation for our problem. The equation we have begun to write is x = half of Tobias’ amount. Now, we just need to insert the numbers that we know of. We know what half is. We can write half as 1/2 or 0.5. We also know Tobias’ amount: it is $4,300. Now we can finish writing our equation: x = 0.5 $4,300.

Step 3: Solve the Equations

The last step in solving a word problem is to solve the equations we wrote. Our problem only had one equation for us to solve. To solve this, we just need to solve for our x . Solving our equation for x just means that we multiply 0.5 with $4,300. Doing that, we find our answer to be $2,150. And we are done!

Another Example

Let’s look at another example. Jenny has a job that she goes to every day after school. She works at the local cupcake shop. She works for 3 hours every day, 15 hours a week. She bakes 200 cupcakes every day! She earns $10 per hour. How much money will she earn after two weeks?

Our first step is to visualize the problem. We picture little Jenny going into the cupcake shop every day and baking her 200 cupcakes. We don’t highlight the 200 cupcakes because we don’t need that information to solve our problem. We do highlight the part that tells us that Jenny works 15 hours every week. We also highlight the part that asks us how much Jenny will make after working for two weeks. We make a note that this is what we are looking for.

Our next step is to write our equations. We understand that the problem is asking us about Jenny’s work for two weeks. We need an equation that tells us how many hours Jenny will work in two weeks. We can label this with an h . So, h = 2 15. Yes, we multiply her weekly hours by two to find her hours for two weeks.

We then need another equation to tell us how much money Jenny will earn in two weeks. We can label this with an x for the information that we want. We need the amount of hours Jenny has worked in two weeks along with her pay. This equation we can write as x = h $10 where x is Jenny’s pay for two weeks.

Our last step is to now solve our equations. We see that we have two equations. One equation requires the answer from the first equation. I go ahead and solve our first equation: h = 2 15 = 30. Now I can solve my second equation by plugging in this information: x = 30 $10 = $300. Ah, my answer is $300. Jenny makes $300 after two weeks. Now I am done.

Lesson Summary

Let’s review now what we’ve learned. To solve word problems , we follow just three simple steps. The first step is to visualize the problem. Included in this first step is also highlighting the important parts of the problem that will help you to solve it.

The second step is to write your equations. You will use the important parts of the word problem to formulate an equation that will help you to solve it. The third and final step is to solve your equations. This is where your algebra skills in solving equations with variables in them come in handy. So, follow this 3-step procedure and don’t let word problems scare you.

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