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Detailed Solution for Word Problem of the Day

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INTRODUCTION

Let's dig into the solution of this one.  Note that this problem is similar to one of the other WPODT.  In fact, this word problem builds upon those concepts. Let me start by saying that, like most math problems, there's more than one way to solve this problem.  At the pre-algebra or middle school math levels it is helpful to conceptualize or "visualize" the problem in a physical sense.  At the algebra level, this problem can be solved using variables.  I will approach the solution at the pre-algebra / middle school level. Please share with us the other ways you or your students have approached solving this problem...

Discussion

Similar to the other WPOTD, there are two questions.  The first question is "How many cookies were initially in the package?" 

To answer this question again requires a fundamental understanding of fractions. We know that 15 cookies were left over.  But what fraction of the package of cookie is this?  Is it 1/2?  Is it 1/4?  It is 3/10.  How can we figure this out?  This is what we first need to find out.  Note that even though the problem does not explicitly ask us this...  Your students should know that this is the first question that must be answered. So to answer that question, we essentially need to add together the fractional parts that were eaten by Robin and Sal then subtract that total from the whole.

When you do this subtraction, you are left with the fractional portion of the package of cookies that remained (3/10). When you know the fractional part & what it represents in numerical terms (15 cookies), you can find the total number of cookies that were in the package.

With all this in mind, the solution looks like this.

 (click image below to enlarge)

The Second Question

Now that we know that there were 50 cookies in the package, finding answers to the second question is very easy.  You simply need to find 1/2 of 50 and 1/5 of 50 to determine the number of cookies Robin and Sal ate respectively.

In doing this you can see that Robin ate 25 cookies and Sal ate 10 cookies.

How did your students approach solving this problem? What are other observations you noticed?  

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