McGraw-Hill Education GRE 2019

Step 3: Combine the equations to solve.

t + s = 20

10 s + 5t = 14 0

Since you are asked to solve for s, you should use the first equation to

write t in terms of s: t = 20 – s. Next, substitute (20 – s) for t in the second

equation:

10 s + 5(20 – s) = 140

Solve for s:

10 s + 5(20 – s) = 140

10 s + 100 – 5s = 14 0

5 s = 40

s = 8

Age Questions

A common type of word problem that gives many students difficulty concerns

age. The approach toward these questions is very similar to what you have looked

at so far, though you will need to keep a couple key facts in mind. Let’s look at an

example:

Bob is 13 years older than Jack. In 3 years Bob will be twice as old as Jack.

How old is Jack?

Step 1: Assign variables. Let j = Jack’s current age and let b = Bob’s current

age.

Before moving on, it is important to understand the emphasis on current

age. In most age questions, you will be given information about the

people’s ages at some earlier or later point. By assigning variables for the

current age, you will be able to express these new ages in terms of the

current ages instead of introducing new variables.

Step 2: Identify relationships.

Relationship 1: Bob is 13 years older than Jack

b = j + 13

Relationship 2: In 3 years Bob will be twice as old as Jack. Bob’s age

in 3 years will be b + 3. Jack’s age in 3 years will be j + 3. Thus you can

construct the following equation: b + 3 = 2(j + 3)

316 PART 4 ■ MATH REVIEW

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