Problem Solving:

What is problem solving? Well, it’s something anyone had better become good at, because life is certainly a never-ending succession of problems, one after another.
Problem solving in mathematics means that a problem, involving numbers and mathematical processes, is described in words, providing information that may or may not be relevant to the solution of the problem and you are required to sort out the information that is helpful and that is unneeded. Working with the “good” data, you then decide which procedure will give you the correct answer and proceed to perform the mathematical calculations to get the result.
Sounds complicated? Not really. First of all, it does not happen very frequently that unnecessary information is included in a word problem as a “red herring” Familiar with the term? If not, you need to read more mystery stories! A red herring is information that proves to be a false clue, following which would lead to the wrong conclusion..Such problems may be assigned in higher grades to intentionally raise the level of complexity, but you don’t have to worry about it now.
Don’t you think though, that it might be helpful to get some practice at looking over a problem, analysing what it is asking you to do, deciding how to go about doing it and then breezing through it? Let us look at an example to give you a sense of what it’s all about:

Two donuts and two coffees cost $5.00. The cost of two coffees and one donut is $4.00. What is the cost of one coffee?
This is really an equation with two unknowns and if you would like to see the “proper”way of solving it, visit our website at www.mathsteps.com, click on the Free Trial, then the Advanced Math and you can learn all about working with the unknowns, equations and equations with two unknowns. For now, let’s keep things simple.
The first and most important thing about solving a problem (whether in math or in life) is: don’t lose your cool. Stay calm, because whenever you try to solve a problem, when you’re all excited, chances are you are going to mess it up. Actually, stay calm for now, because you will have the opportunity to see how it should be done and if you notice in the Free Trial, solutions are provided for any and every problem assigned - so don’t worry - you’re not in the dark! The more you do this and the more practice you get, the calmer you will be, because you will know that you have done it before and you can do it again!

O.K. Let’s take a look at this problem. We are told that two coffees and two donuts cost $5.00 and two coffees and one donut are $4.00. What is the difference between the two situations?
Well obviously the difference is $1.00, since five minus four equals one or

But there is something else that is different: we are one donut short in the second instance. In the first, we have two coffees and two donuts, in the second we have two coffees and only one donut. The two coffees are the same, but we have two donuts in the first instance minus one donut in the second, leaving one donut “missing” or “short”.

That means that the difference of “one donut” will have the same value as the difference of $1.00 and we can therefore state that a donut costs $1.00.
If we now go back to the “two coffees and one donut cost $4.00" statement and subtract the cost of the donut of $1.00:

So that the cost of two coffees alone must be $3.00 To calculate the cost of one coffee, we divide by 2:

And that will give us the cost of one coffee as $1.50.

This is most likely all very obvious to you and you are undoubtedly almost bored to sleep by all the unnecessary detail, but we wanted to make sure that the procedure would explained step by step. To see more problems like this and tougher (and much tougher), visit us at www.mathsteps.com, click on Free Trial, then Basic Math and have fun!