Math Word Problems for Armed Services Vocational Aptitude Battery (ASVAB) Study Guide
Many of the math problems on tests are word problems. A word problem can include any kind of math, including simple arithmetic, fractions, decimals, percentages, even algebra and geometry.
The hardest part of any word problem is translating English into math. When you read a problem, you can frequently translate it word for word from English statements into mathematical statements. At other times, however, a key word in the word problem hints at the mathematical operation to be performed. Here are the translation rules:
Distance Formula: Distance = Rate x Time
The key words are movement words like: plane, train, boat, car, walk, run, climb, swim.
- How far did the plane travel in 4 hours if it averaged 300 miles per hour?
- d = 300 × 4
- d = 1,200 miles
- Ben walked 20 miles in four hours. What was his average speed?
- 20 = r × 4
- 5 miles per hour = r
Solving a Word Problem Using the Translation Table
Remember the problem at the beginning of this chapter about the jellybeans?
- 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?
We solved it by working backward. Now let's solve it using our translation rules.
Assume Juan started with J jellybeans. Eating of them means eating jellybeans. Maria ate a fraction of the remaining jellybeans, which means we must subtract to find out how many are left: Maria then ate , leaving of the jellybeans, or jellybeans. Multiplying out gives J as the number of jellybeans left. The problem states that there were 10 jellybeans left, meaning that we set equal to 10:
Solving this equation for J gives J = 60. Thus, the right answer is a (the same answer we got when we worked backward). As you can see, both methods—working backward and translating from English to math—work. You should use whichever method is more comfortable for you.
Practice Word Problems
You will find word problems using fractions, decimals, and percentages in those sections of this chapter. For now, practice using the translation table on problems that just require you to work with basic arithmetic.
- Amir went shopping with $250 and returned home with only $33.56. How much money did he spend?
- Mark invited ten friends to a party. Each friend brought three guests. How many people came to the party, excluding Mark?
- The office secretary can type 75 words per minute. How many minutes will it take him to type a report containing 1,200 words?
- Mr. Wallace is writing a budget request to upgrade his personal computer system. He wants to purchase a cable modem, which will cost $100, two new software programs at $350 each, a color printer for $249, and an additional color cartridge for $25.What is the total amount Mr. Wallace should write on his budget request?