Learning Objectives
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 on). 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 Polya, known 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.
Tutorial
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.
Since we are looking for a number, we will let
x = a number
*Get all the x terms on one side
*Inv. of sub. 2 is add 2
FINAL ANSWER:
We are looking for two numbers, and since we can write the one number in terms of another number, we will let
x = another number
one number is 3 less than another number:
x - 3 = one number
*Inv. of sub 3 is add 3
*Inv. of mult. 2 is div. 2
FINAL ANSWER:
Another number is 87.
Perimeter of a rectangle = 2(length) + 2(width)
We are looking for the length and width of the rectangle. Since length can be written in terms of width, we will let
w = width
length is 1 inch more than 3 times the width:
1 + 3w = length
*Inv. of add. 2 is sub. 2
*Inv. of mult. by 8 is div. by 8
FINAL ANSWER:
Length is 10 inches.
Complimentary angles sum up to be 90 degrees.
We are already given in the figure that
x = 1 angle
5x = other angle
*Inv. of mult. by 6 is div. by 6
FINAL ANSWER:
The two angles are 30 degrees and 150 degrees.
Practice Problems
To get the most out of these, you should work the problem out on your own and then check your answer by clicking on the link for the answer/discussion for that problem. At the link you will find the answer as well as any steps that went into finding that answer.
Practice Problems 1a - 1c: Solve the word problem.
Need Extra Help on these Topics?
http://www.purplemath.com/modules/ageprobs.htm
This webpage goes through examples of age problems, which are like
the numeric problems found on this page.
Go to Get Help Outside the Classroom found in Tutorial 1: How to Succeed in a Math Class for some more suggestions.
Last revised on July 26, 2011 by Kim Seward.
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