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ASVAB Math Tip 2 - Word Problems

Many students have an unnecessary fear of word problems (such as those found in the Arithmetic Reasoning section of the ASVAB). However there are some tricks that will help you quickly translate the words into a math problem.

A LOT of word problems can be solved using CROSS-MULTIPLICATION

The first step is to re-state the problem in this way: " ________ IS TO________ AS ________ IS TO ________ ."

Here's a simple example.

Example 1) If 3 pounds of onions cost $0.90, how much will 10 pounds cost?

Step 1 - Reword this as "3 pounds is to $.90 as 10 pounds is to ?"
Step 2 - Write this as a cross multiplation problem: 3/.90 = 10/x Notice I replaced "IS TO" with a division sign, "AS" with an equal sign, and "?" with x.

Step 3 - Now cross multiply and solve: 3*x = .90 * 10
3x = 9
x = 9/3
x = $3

* * *

Here are some more examples. Notice the variety of problems that can solved with cross multiplication!

Example 2) A worker can assemble 15 widgets in 6 hours. At this rate, how many can the worker assemble in a 40-hour work week?

Step 1 - Reword: "15 is to 6 hours as ? is to 40 hours"
Step 2 - Set up problem: 15/6 = x/40
Step 3 - Now cross multiply and solve: 15 * 40 = 6x
600 = 6x
x = 600/6
x = 100

* * *

The following example is explicitly stated as a ratio. And ratios are classic "ISTO/AS" problems.

Example 3) The ratio of boys to girls at a school is 6 to 5. How many girls are there if there are 3600 boys?

Step 1 - Reword: "6 boys is to 5 girls as 3600 boys is to ? girls"
Step 2 - Set up problem: 6/5 = 3600/x
Step 3 - Now cross multiply and solve: 5 * 3600 = 6x
18000 = 6x
x = 18000/6
x = 3000

* * *

Sometimes you have to do some quick conversions to get the same units, e.g. hours to minutes, feet to inches.

Example 4) Riding your bike you travel 1 mile in 10 minutes. At this same pace, how far will you go in 2 hours?

Step 1 - Reword: "1 mile is to 10 minutes as ? miles is to 2 hours" Converting hours to minutes this is: "1 mile is to 10 minutes as ? miles is to 2*60 minutes"
Step 2 - Set up problem: 1/10 = x/120
Step 3 - Now cross multiply and solve: 1 * 120 = 10 * x
x = 120/10
x = 12

* * *

Getting comfortable with this 'ISTO/AS' format will help you solve a wide range of word problems.

And remember to look at your answer and do a quick reasonability check to catch blatant calculation errors!

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