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Solving Problems With the Guess, Check & Revise Method

Instructor: Laura Pennington

Laura has taught collegiate mathematics and holds a master's degree in pure mathematics.

In this lesson, we will look at how to solve problems using the guess, check, and revise method in mathematics. Through examples, we will look at each step involved and see exactly how this process works.

Guess...What?

Everybody has come across a time in their life when they have been saving up for something. For instance, my friend Amy, who is a triathlete, has been saving up for a new bike for a few months now. She's $400 from her goal, so she decided to make a whole bunch of brownies and cookies to sell. She has enough ingredients to make 137 baked goods, and she's charging $5 for a brownie and $2 for a cookie. She's trying to figure out how many of each she needs to make and sell to reach her goal of $400.


Problem
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She starts by considering if she made 68 brownies and 69 cookies (about the same of each and there are 137 baked goods total). In this case, she would make 68*5 = $340 from brownies and 69*2 = $138 from cookies giving a total of 340 + 138 = $478. This is a bit too much, so she increases the number of cookies to 80 and decreases the number of brownies to 57, because 80 + 57 = 137, giving 80*2 + 57*5 = $445. Still just a bit high, so she adjusts again by increasing the number of cookies to 95 and decreasing the number of brownies to 42 giving 95*2 + 42*5 = $400. Ah-ha! That's exactly what she wanted!


Guesses
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Here's an interesting fact! The process she just used to figure out how many brownies and cookies to make and sell is a well-known solving process in mathematics called the guess, check, and revise method.

This method has three components, or steps, and they are exactly as the name suggests:

  1. Guess
  2. Check
  3. Revise

The Steps Explained

The first step in the guess, check, and revise method is to make an educated guess. Hmmm, what does it mean to make an educated guess? Notice, in our opening example, Amy's first guess was 68 brownies and 69 cookies. While this is a guess, it's not just two numbers she randomly pulled out of thin air. She knew that she had enough ingredients to make 137 baked goods, so she knew that the two numbers had to add up to 137, then she started somewhere in the middle. She used the information given to make a guess that made sense with the problem - this is an educated guess.


Step One
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Once an educated guess has been made, we want to check to see if that guess is correct. In other words, does it solve the problem? After Amy made a guess of 68 brownies and 69 cookies, she then checked to see if this would get her the $400 she wants. That explains the second step of the method, which brings us to the last step - revise.


Step Two
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Our third step is to revise our guess by making a new guess. We have a bit more information at this point so we can use it to make an even better guess. When Amy realized that her first guess of 68 brownies and 69 cookies resulted in $478, she knew this was too much, so when she revised her guess, she increased the cheaper option and decreased the more expensive option. She made a revised guess based on the new information she got from her last guess.


Step Three
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We know that she repeated this process until she got the right answer. This is all there is to it when it comes to the guess, check, and revise method. That's not so hard, is it? We just do exactly as the name suggests - guess, check, and revise!

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