Education.com

# Math Strategies for Firefighter Exam Study Guide (page 3)

By LearningExpress Editors
LearningExpress, LLC

### Working Backward

You can frequently solve a word problem by plugging the answer choices back into the text of the problem to see which one fits all the facts stated in the problem. The process is faster than you think because you will probably only have to substitute one or two answers to find the right one.

This approach works only when:

• All of the answer choices are numbers.
• You are asked to find a simple number, not a sum, product, difference, or ratio.

Here's what to do:

1. Look at all the answer choices and begin with one in the middle of the range. For example, if the answers are 14, 8, 20, and 25, begin by plugging 14 into the problem.
2. If your choice doesn't work, eliminate it. Determine if you need a bigger or smaller answer.
3. Plug in one of the remaining choices.
4. If none of the answers work, you may have made a careless error. Begin again or look for your mistake.
Example: Juan ate of the jellybeans. Maria then ate of the remaining jellybeans, which left 10 jellybeans. How many jellybeans were there to begin with?
1. 60
2. 90
3. 120
4. 140

Starting with one of the middle answers, let's assume there were 90 jellybeans to begin with:

Since Juan ate of them, that means he ate 30 ( × 90 = 30), leaving 60 of them (90 – 30 = 60).Maria then ate of the 60 jellybeans, or 45 of them ( × 60 = 45). That leaves 15 jellybeans (60 – 45 = 15).

The problem states that there were 10 jellybeans left, and you wound up with 15 of them. That indicates that you started with too big a number. Thus, 90, 120, and 140 are all wrong! So, let's try 60:

Since Juan ate of them, that means he ate 20 ( × 60 = 20), leaving 40 of them (60 – 20 = 40).Maria then ate of the 40 jellybeans, or 30 of them ( × 40 = 30). That leaves 10 jellybeans (40 – 30 = 10).

The right answer is a, because this result of 10 remaining jellybeans agrees with the problem.

### Ask a Question

150 Characters allowed

### Related Questions

#### Q:

See More Questions

### Today on Education.com

#### WORKBOOKS

May Workbooks are Here!

#### ACTIVITIES

Get Outside! 10 Playful Activities