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Learning Objectives After completing this tutorial, you should be able to: Use Polya's four step process to solve word problems involving s, percents, rectangles, supplementary angles, complementary angles, consecutive integers, and breaking even. Introduction Whether you like it or not, whether you are going to be a mother, father, teacher, computer programmer, scientist, researcher, business owner, coach, mathematician, manager, doctor, lawyer, banker the list can go on and onproblem solving is everywhere.

Some people think that you either can do it or you can't. Contrary to that belief, it can be a learned trade. Even the best athletes and musicians had some coaching along the way and lots of practice. That's what it also takes to be good at problem solving.

George Polyaknown as the father of modern problem solving, did extensive studies and wrote numerous mathematical papers and three books about problem solving.

I'm going to show you his method of problem solving to help step you through these problems. Just note that your math teacher or math book may word it a little differently, but you will see it all basically means the Looking for w 45 thing. If you follow these steps, it will help you become more successful in the world of problem solving.

Polya created his famous four-step process for problem solving, which is used all over to aid people in problem solving:. Step 1: Understand the problem. Step 2: Devise a plan translate. Step 3: Carry out the plan solve.

Step 4: Look back check and interpret. Just read and translate it left to right to set up your equation. We are looking for two s, and since we can write the one in terms of anotherwe will let. Another is We are looking for how many students passed the last math test, we will let. We are looking for the price of the tv before they added the tax, we will let.

We are looking for the length and width of the rectangle. Since length can be written in terms of width, we will let. Length is 10 inches. If we let x represent the first integer, how would we represent the second consecutive integer in terms of x? Well if we look at 5, 6, and 7 - note that 6 is one more than 5, the first integer.

And what about the third consecutive integer. Well, note how 7 is 2 more than 5. Consecutive EVEN integers are even integers that follow one another in order. If we let x represent the first EVEN integer, how would we represent the second consecutive even integer in terms of x? Note that 6 is two more than 4, the first even integer. And what about the third consecutive even integer? Well, note how 8 is 4 more than 4.

Consecutive Looking for w 45 integers are odd integers that follow one another in order. If we let x represent the first ODD integer, how would we represent the second consecutive odd integer in terms of x? Note that 7 is two more than 5, the first odd integer. And what about the third consecutive odd integer? Well, note how 9 is 4 more than 5. Note that a common misconception is that because we want an odd that we should not be adding a 2 which is an even.

Keep in mind that x is representing an ODD and that the next odd is 2 away, just like 7 is 2 away form 5, so we need to add 2 to the first odd to get to the second consecutive odd. In the revenue equation, R is the amount of money the manufacturer makes on a product. If a manufacturer wants to know how many items must be sold to break even, that can be found by setting the cost equal to the revenue.

At the link you will find the answer as well as any steps that went into finding that answer. Practice Problems 1a - 1g: Solve the word problem. Need Extra Help on these Topics? After completing this tutorial, you should be able to: Use Polya's four step process to solve word problems involving s, percents, rectangles, supplementary angles, complementary angles, consecutive integers, and breaking even.

Whether you like it or not, whether you are going to be a mother, father, teacher, computer programmer, scientist, researcher, business owner, coach, mathematician, manager, doctor, lawyer, banker the list can go on and onproblem solving is everywhere. Sometimes the problem lies in understanding the problem. If you are unclear as to what needs to be solved, then Looking for w 45 are probably going to get the wrong.

In order to show an understanding of the problem, you, of course, need to read the problem carefully. Sounds simple enough, but some people jump the gun and try to start solving the problem before they have read the whole problem. Once the problem is read, you need to list all the components and data that are involved. This is where you will be asing your variable.

When you devise a plan translateyou come up with a way to solve the problem. Setting up an equation, drawing a diagram, and making a chart are all ways that you can go about solving your problem. In this tutorial, we will be Looking for w 45 up equations for each problem. The next step, carry out the plan solveis big. This is where you solve the equation you came up with in your 'devise a plan' step. The equations in this tutorial will all be linear equations. If you need help solving them, by all means, go back to Tutorial 7: Linear Equations in One Variable and review that concept.

You may be familiar with the expression 'don't look back'. In problem solving it is good to look back check and interpret. Basically, check to see if you used all your information and that the answer makes sense. If your answer does check out, make sure that you write your final answer with the correct labeling. A lot of numeric types of word problems revolve around translating English statements into mathematical ones.

Example 1 : Twice the difference of a and 1 is 4 more than that. Find the. If you take twice the difference of 6 and 1, that is the same as 4 more than 6, so this does check. Example 2 : One is 3 less than another. If the sum of the two s isfind Looking for w 45. If we add 90 and 87 a 3 less than 90 we do get Whenever you are working with a percent problem, you need to make sure you write your percent in decimal form. You do this by moving the decimal place of the percent two to the left.

Example 4 : A math class has 30 students. How many students passed the last math test? If the tax rate is 8. Example 6 : In a blueprint of a rectangular room, the length is 1 inch more than 3 times the width. Find the dimensions if the perimeter is to be 26 inches. Make sure that you read the question carefully several times. If width is 3, then length, which is 1 inch more than 3 times the width would have to be The perimeter of a rectangle with width of 3 inches and length of 10 inches does come out to be Example 7: Find the measure of each angle in the figure below.

Note that since the angles make up a straight line, they are supplementary to each other. Consecutive integers are integers that follow one another in order. For example, 5, 6, and 7 are three consecutive integers. For example, 4, 6, and 8 are three consecutive even integers. For example, 5, 7, and 9 are three consecutive odd integers.

Example 8: The sum of 3 consecutive integers is Find the integers. Example 9: The ages of 3 sisters are 3 consecutive even integers. If the sum of twice the 1st even integer, 3 times the 2nd even integer, and the 3rd even integer is 34, find each age. If we take the sum of two times 4, three times 6, and 8, we do get In a business related problem, the cost equation, C is the cost of manufacturing a product. When x is 5 the cost and the revenue both equal These are practice problems to help bring you to the next level.

It will allow you to check and see if you have an understanding of these types of problems.

Math works just like anything else, if you want to get good at it, then you need to practice it. Even the best athletes and musicians had help along the way and lots of practice, practice, practice, to get good at their sport or instrument. In fact there is no such thing as too much practice. The sum of a and 2 is 6 less than twice that. A local furniture store is having a terrific sale. How much would you save if you bought it at this sale? A rectangular garden has a width that is 8 feet less than twice the length.

Find the dimensions if the perimeter is 20 feet. Complimentary angles sum up to be 90 degrees. Find the measure of each angle in the figure below.

Note that since the angles make up a right angle, they are complementary to each other. The sum of 3 consecutive odd integers is

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