Here's the problem as written: The ratio of the number of John's pencils to Mike's pencils is 7:3. John has 32 more pencils than Mike. If John gives 1/4 of his pencils to Mike, what will the new ratio be?
I don't even know where to begin with this one. I would like to know how to go about solving this type of problem in the future as I am sure it will show up on a test! Thank you.
There is no formula for this type of problem. There is, however, a method to use on all word problems. This problem is a little tricky because it is really two problems in one. To find out what is going on when the number of pencils held by each boy changes, you need to know how many pencils each has to begin with. Make sense? So let's start with the first problem
First, ALWAYS start by writing down a concise definition of each variable that MAY be relevant and assigning a unique letter to that variable. tkhunny did that for you in his post. Make a habit of doing this. At the very least, it is getting one thing out of your head onto paper.
Second, identify any pieces of general information that you are expected to know and write them down using the letters that you selected in the first step. In this problem, the general information that you are expected to know is how to express a ratio between John's pencils and Mike's pencils. Do you know how to express a ratio in mathematical form? Also identify and write down any equalities that apply.
Third, identify any pieces of information that are specific to this problem and write them down using the letters you selected in the first step. The specific information in this problem is how many more pencils John has than Mike does. Do you know how to express that in mathematical form? Also write down any equalities that apply.
At this point you should have two equations in two variables. What are they? Do you know how to solve them? If so, what answers do you get? Now check your work.
If it checks, you are ready to tackle the second problem of this double-barreled problem. You already have definitions and symbols for your variables. You already know how to express a ratio. Write down using your letters the proper ratio. But you know what numbers the letters stand for so what does that ratio equal?
It is a very methodical, step-by-step process that works for every word problem.
Try it. Let us know where you get stuck or ask us to review your work.
