Detailed Solution for Word Problem of the Day


Like it or not your students will come in contact with one of these types of math problems on their math exams as they progress through to high school, college, and beyond.  As before, this problem must be read carefully, then translated to the equivalent math equation that it represents.  After doing that, arithmetic and algebraic techniques must be used to solve the equation.  Enjoy...

(click image below to enlarge)

How to dissect this problem

Translating this problem to the equivalent math equation requires students to read one section of the problem at a time and write down the math representation as they go along.  If this may sound familiar, that's because it is.  Click here to see my previous post regarding translating word problems to math equations.


The goal of this problem is to find a math expression to represent the Jaden's age if Nancy's age is given to us.  In other words, if we knew Nancy's age what is Jaden's age? There is a relationship between their ages therefore if we know one of their ages we can figure out the other's age based on the relationship between the ages that we know.  The challenge is to properly interpret (or translate) the relationship that is given to us in the word problem.  Let's take a closer look at this problem step by step.

Step 1: This is the most important step because if is not captured correctly then the rest of the problem will not be correct.

"If Jaden's age is increased by Nancy's age..."

The student should stop right here, process this piece of information, make sure they understand this piece of information, then right down the math representation of this piece of information. The word "increased" is a keyword that translate to add:

J + N

After this information has been properly processed and understood, then they should move on with processing more information from the problem.

"the result is"

The word "is" is another keyword which translates to "equal".  So we get:

J + N =

So far so good... Let's read on to see what else is there.

"2.5 times"

Now were talking about multiplying 2.5 times "somthing", so we could write it down like this:


J + N = 2.5("something")

The "something" is "Jaden's age 6 years ago".  To translate this phrase we simply need to realize that "6 years ago" means to subtract. Furthermore, we are subtracting 6 years from Jaden's age.  Therefore the "something" looks like this:

J - 6

Once this information is plugged into the main equation, the full resulting math equation looks like this:

J + N = 2.5(J - 6)

As I said this is the most important step because if this math equation has not been translated correctly, then the entire problem will be calculated incorrectly.


We can now move on to step 2, 3 & 4 where what we are basically doing is solving the equation in step 1 for J


How did your students approach solving this problem? What are other observations you noticed?  Let us know below...

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  • Auden

    wow! this is soooo insightful – the math modeling is the key!