Writing+Equations+from+Word+Problems

Word problems are one of the trickiest part of the Regents. Often times we know how to do the math, but breaking down the word problem to get to the math is difficult. In this lesson, you will learn how to identify the two main types of word problems and learn strategies for how to address each type of word problem.


 * The Two Main Types of Word Problem**

1. The first type of word problem is a problem where a**ll of the information you need to solve the problem is given** in the problem and you have to **figure out a way to put all of the information together** to find the solution. An example of this type of problem is:

A bag contains eight green marbles, five white marbles, and two red marbles. What is the probability of drawing a red marble from the bag?

In this problem, they give us everything we need to know in order to find the probability. We just have to remember how to write out probability and put all of the information they give us together to find our solution (we'll talk more about this below and in the next lesson).

2. The second type of word problem is a problem where there is **some piece of information that is missing** from the problem. In this type of problem you will **need a variable** to represent the missing information and use the words in the problem to **write an equation or expression**. An example of this type of problem is:

Tamara has a cell phone plan that charges $0.07 per minute plus a monthly fee of $19.00. She budgets $29.50 per month for total cell phone expenses without taxes. What is the maximum number of minutes Tamara could use her phone each month in order to stay within her budget?

In this problem, they leave out an important piece of information, which is how many minutes she talks on the phone. Therefore, we're going to have to use a variable to represent this and write an equation or expression (we'll talk more about this below and in the next lesson).


 * How do we break down each type of problem?**


 * 1. When all the information needed is given:** In this type of problem, we need to figure out how we will use the information given in the problem to find what the question is asking for. We can use this chart to help us break down these types of word problems (reading the headings carefully because they are slightly different from the headings we've used in these charts before):

- any important information - what the question is asking for || - what else do we need to know in order to answer the question || - put the information from the first column together with what you already know about math to find the information you said you needed in the second column ||
 * ~ What important information is given in the problem? ||~ What do we need to know that they do not tell us in the problem? ||~ How do we use the important information and our knowledge of math to find the things we need to know (in column 2)? ||
 * - key words

Let's take a look at the example from above:

A bag contains eight green marbles, five white marbles, and two red marbles. What is the probability of drawing a red marble from the bag?

5 white marbles 2 red marbles probability of drawing a red marble? || How many marbles there are total How do we write probability? || There are 15 marbles total We write probability as a fraction with the number of red marbles in the numerator and the total number of marbles in the denominator. ||
 * ~ What important information is given in the problem? ||~ What do we need to know that they do not tell us in the problem? ||~ How do we use the important information and our knowledge of math to find the things we need to know (in column 2)? ||
 * 8 green marbles

Notice that we did not SOLVE the problem, but just broke it down so that we're ready to solve it. We'll solve the word problems in the next lesson.


 * 2. When there's some piece of information missing:** In this type of problem, we need to figure out what our variable is going to represent and then write the equation. For this type of problem, there 2 steps to get the problem ready to solve.

Step 1: Define you variable - This means choose a variable and state what it represents (for example, x = minutes or n = area) Step 2: Translate the words from the problem into math. Use the variable that you defined in step 1. At the end of this step, you should have either an equation that you can solve or an expression that you can simplify.

Let's take a look at the example from the beginning of the lesson:

Tamara has a cell phone plan that charges $0.07 per minute plus a monthly fee of $19.00. She budgets $29.50 per month for total cell phone expenses without taxes. What is the maximum number of minutes Tamara could use her phone each month in order to stay within her budget?

Step 1: Define the variable.

x = number of minutes

Step 2: Translate the words from the problem into math.

0.07x + 19 = 29.50

Again, we did not solve the problem, we just set it up. We'll worry about solving word problems in the next lesson.


 * So to re-cap:**

When solving word problems, we first need to determine what type of word problem we have (do they give us everything we need to know or is there something missing?). Then, if they give us everything we need to know, we can use the chart to break down the problem. If there's something missing, we need to define our variable and write out an equation or expression that represents the problem.

**TASK: For each of the following problems, state which type of word problem they are/which method you are going to use to solve them. Explain in words how you determined which type of word problem they are.**

1. 2.

3.

4.

**TASK: Open the document below and break down (YOU DO NOT NEED TO SOLVE) each problem using the two methods discussed in this lesson. **