McGraw-Hill Education GRE 2019

Create algebraic relationships!

Once you’ve created relationships, you can then use your algebra skills to solve

the problem. Let’s look at a typical word problem and a step-by-step methodology

for creating these algebraic relationships.

The sum of the lengths of two pipes is 70 feet. The length of the longer piece

is 20 feet more than the length of the shorter piece. What is the length of the

shorter piece?

Step 1: Identify your unknowns. An unknown is any quantity with an

unspecified value. An unknown can be something like Bob’s age, Jack’s

height, the number of people in a room, and so on. In the preceding question,

there are two unknowns: the length of the shorter pipe and the length of the

longer pipe.

Step 2: Assign variables to the unknowns. Since your ultimate goal is

to derive algebraic relationships, you should express your unknowns as

variables: Let l = the length of the longer pipe and let s = the length of the

shorter pipe. You can use other letters as well, but it is helpful to use letters

that help you remember which unknown the variable refers to (in this case,

you can use l for “longer” and s for “shorter”).

Step 3: Identify relationships among the unknowns. This is the final step in

going from words to algebra. Once you identify a relationship, you can create

an equation or inequality and start solving for your variables. Words such as

is, equals, is greater, and is less are helpful indicators of relationships. In the

previous example, there are two relationships among the variables:

Relationship 1: The sum of the lengths of two pipes is 70 feet. Since

sum means addition, you should interpret this information to mean

the length of the shorter pipe + length of the longer pipe = 70

Using variables: ↓ ↓

l + s = 70

Relationship 2: The length of the longer piece is 20 feet greater than the

length of the shorter piece. The word is indicates a relationship between

l and s. On your paper, write down:

l = s

Now translate the wording “20 feet greater.” Since the longer piece is 20

feet more than the shorter piece, it must be true that s alone is not enough

to equal l. Thus to make the two sides of the equation equal, you must add

20 to s:

l = s + 20

314 PART 4 ■ MATH REVIEW

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