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Dealing with Word Problems Study Guide (page 3)

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Updated on Oct 4, 2011

DISTANCE FORMULA: DISTANCE = RATE × TIME

Look for key words like plane, train, boat, car, walk, run, climb, swim, travel, and move.

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 4 hours. What was his average speed?

20 = r × 4

5 miles per hour = r

Using the Translation Rules

Here's an example of how to solve a word problem using the translation table.

Example: Carlos ate of the jelly beans. Maria then ate of the remaining jelly beans, which left 10 jelly beans. How many jelly beans were there to begin with?

a. 60

b. 80

c. 90

d. 120

e. 140

Here's how we marked up the question and took notes as we read it. Notice how we used abbreviations to cut down on the amount of writing. Instead of writing the names of the people who ate jelly beans, we used only the first letter of each name; we wrote the letter j instead of the longer word, jelly bean.

Example: Carlos ate of the jelly beans. Maria then ate of the remaining jelly beans, which left 10 jelly beans. jelly beans were there

C =

M = remaining

10 left

The following straightforward approach assumes a knowledge of fractions and elementary algebra. With the previous lessons under your belt, you should have no problem using this method. However, the same problem is presented in the next lesson, but it is solved by a backdoor approach, working backward, which does not involve algebra.

What we know:

  • Carlos and Maria each ate jelly beans.
  • Carlos ate of the jelly beans.
  • Maria then ate of the jelly beans that Carlos left.
  • Afterward, there were 10 jelly beans.

The question itself: How many jelly beans were there to begin with?

Plan of attack:

  • Find out how many jelly beans Carlos and Maria each ate.
  • Add 10, the number of jelly beans that were finally left, to get the number of jelly beans they started with.

Solution:

Let's assume there were j jelly beans when Carlos started eating them. Carlos ate of them, or jelly beans (of means multiply). Since Maria ate a fraction of the remaining jelly beans, we must subtract to find out how many Carlos left for her: j = j. Maria then ate of the j. jelly beans Carlos left her, or × j. jelly beans, which is .Altogether, Carlos and Maria ate + jelly beans, or jelly beans. Add the number of jelly beans they both ate ()to the 10 leftover jelly beans to get the number of jelly beans they started with, and solve the equation:

+ 10=j

10 = j

10 =

60 = j

Thus, there were 60 jelly beans to begin with.

Check: We can most easily do this by plugging 60 back into the original problem and seeing if the whole thing makes sense.

Carlos ate of 60 jelly beans. Maria then ate of the remaining jelly beans, which left 10 jelly beans. How many jelly beans were there to begin with?

Carlos ate of 60 jelly beans, or 20 jelly beans (×60=20).That left 40 jelly beans for Maria (60 – 20 = 40). She then ate of them, or 30 jelly beans ( × 40 = 30). That left 10 jelly beans (40 – 30=10), which agrees with the problem.

Tip

The next time you walk into a clothing or department store, bring a notepad and look around for a discount sign of a percentage taken off the regular price of a product. First, write down the full price of the item. Then, create a word problem that asks what dollar amount you'd save if you bought the item with that percentage discount. After you create the word problem, try solving it.

Dealing with Word Problems Sample Question

Four years ago, the sum of the ages of four friends was 42 years. If their ages were consecutive numbers, what is the current age of the oldest friend?

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