#### The Process for Word Problems

Underneath the convoluted language in SAT word problems are really just simple math concepts. It is easy to get lost in the words and fail to see the manageable math equations.

The SAT rarely asks questions that are simple and straightforward. Expect problems that require you to convert complex written statements into variables and equations.

*If you tripled Adam’s age, he would be double Frank’s age. Frank is currently 9 years old.*

This translates into the equation:

3*a*/2 = 9

The most effective strategy for solving a word problem is to express the question as an equation or relationship where *x*, or some other letter, represents the quantity that you need to find.

800score Tip

Many algebra word problems contain several variables. It is helpful to track the variables by using letters that correspond to the items in the question. For example, if the question is about Adam, use the variable “

a.”

#### The 5 Steps

**1) Read the Question**

Read and re-read the question until it makes sense. You might need to rephrase the question into your own words, or break the question into simpler parts. Just make sure you know exactly what the question is asking.

As you read the question, be on the lookout for tricks, traps or anything unusual.

**2) Read the Answers**

Look at the answers before working on a solution. The SAT often makes questions appear more complicated than they really are, so the answers can clarify your understanding of the question. For example, reading the answers can prevent you from solving for the wrong variable. You can also see how exact your answer needs to be. Can you estimate and use rounding? Can you factor then cancel?

The SAT often requires you to convert units, so reading the answers will help ensure you use the right units.

**3) Define Variables and Relationships**

Choose meaningful letters that will help you keep the variables straight.

Look for words that define relationships and actions, such as “twice as many”, “combined,” “gives,” or “greater than.” More examples of words that show relationships and actions are in the next section and throughout this chapter.

**4) Choose a Technique and Apply It**

Your goal when taking the SAT is to pick the right answers on a multiple-choice exam. You are not being graded on style. It doesn’t matter if you find the answer following the usual routine. In fact, the fastest way to an answer often does not involve using a traditional method, but rather a method geared specifically to the SAT.

Each question may have several possible approaches, so you need to develop an ability to recognize a fast and effective way to solve different question types. Once you have chosen a technique, run the numbers and follow your plan. If it is taking too long, see if you can find shortcuts on the math or change your technique. Go back to Step 1 and reread the question and answers, if necessary.

1. Plow

2. Don’t Do That Math!

3. Backsolving

4. Plug-In

5. Ballpark

6. Experiment

7. Pattern

**5) Eliminate Choices**

Picking the correct answer choice may not require a complete solution to the problem. Eliminating all the wrong answers is the same as finding the right answer.

If you don’t know an answer, you CANNOT skip the question and return to it later. But don’t just guess a random answer, make an educated guess.

Use the process of elimination to decrease the number of possible answers choices, even if you can’t find the exact answer. Use logic to rule out wrong answers. With every answer choice you can eliminate, you increase your odds of guessing correctly.

You have to guess aggressively on the SAT. When a question is clearly too tough, make an educated guess and move on. Don’t get stuck on one problem. Take the time you would have wasted on that problem and use it on a question you know how to solve.

The techniques in the next section will give you tools you can use to eliminate wrong answer choices.

**How to Eliminate Choices**

Video Courtesy of **Kaplan SAT prep.**

**The examples below illustrate The 5 Steps. **

ExampleA library is having a book sale. Hardcover books cost $4 each and paperbacks cost $2 each. Lisa spent $28 for 8 books. How many hardcover books and how many paperback books did she purchase?

### Solution

The question is looking for two numbers: the numbers of hardcover and paperback books.

Define the variables and write equations based on the given information. Let *h* be the number of hardcovers and *p* be the number of paperbacks.

She bought 8 books, so *h* + *p* = 8.

Since hardcover books cost $4, the total cost of *h* hardcovers is 4*h*.

Paperback books cost $2, so the cost of *p* paperbacks is 2*p*.

She spent $28, so 4*h* + 2*p* = 28.

*h* + *p* = 8

4*h* + 2*p* = 28

*Method 1: Substitution*

Solve for *h*: *h* = 8 − p

Substitute:

4*h* + 2*p* = 28

4(8 − *p*) + 2*p* = 28

32 − 4*p* + 2*p* = 28

-2*p* = -4

*p* = 2 paperback books

Substitute:

*h* + *p* = 8

*h* + 2 = 8

*h* = 6 hardcover books

*Method 2: Addition*

Multiply the first equation by 4:

4*h* + 4*p* = 32

Subtract:

4*h* + 4*p* = 32

− [4*h* + 2*p* = 28]

2*p* = 4

*p* = 2 paperback books

Substitute:

*h + p* = 8

*h + 2* = 8

*h *= 6 hardcover books

ExampleThere are 15 marbles. There are twice as many white marbles as the number of green and blue marbles combined. One fifth of the marbles are green. How many marbles of each color are there?

### Solution

Define the variables. Let *w* be the number of white marbles, *g* the number of green marbles and *b* the number of blue marbles.

Write an equation based on each sentence of the question.

15 = *w* + *g* + *b*

*w* = 2(*g* + *b*)

*g* = (1/5)(15)

*g* = 3

Substitute *g* = 3 into both of the other equations, then simplify.

15 = *w* + 3 + *b*

12 = *w* + b

*w* = 2(3 +* b*)

*w* = 6 + 2*b*

Substitute *w* = 6 + 2*b* into the first equation.

12 = 6 + 2*b* + *b*

6 = 3*b*

*b* = 2

Substitute *g* = 3 and *b* = 2 into the original first equation.

15 = *w* + 3 + 2

*w* = 10

There are 3 green marbles, 2 blue marbles and 10 white marbles.

ExampleThe area of a triangle is 15 and the base is 10. What is the height of the triangle?

### Solution

Use the formula

A = 1/2 *bh*

15 = 1/2 (10)*h*

15 = 5*h*

*h* = 3