GED Word Problems: The Complete "How to Solve" Guide

GED Word Problems: The Complete "How to Solve" Guide

(1,200+ words – Every line is actionable under timed conditions)

Introduction

"Word problems appear 8–10 times on the GED Math test—master them, and you’ll gain 20+ raw points, moving you from a 145 to a 165+ score. This isn’t about math; it’s about reading for the right clues and making one smart decision per step."

WHAT THIS QUESTION TYPE IS ACTUALLY TESTING

The GED isn’t testing your ability to do algebra—it’s testing: - Reading for structure: Can you extract the exact relationship between quantities? - Decision discipline: Can you avoid the trap of "plugging in numbers" before defining variables? - Elimination logic: Can you spot the 4 wrong-answer patterns before solving?

ANATOMY OF THE QUESTION

Structure Breakdown

Representative Example

A bakery sells cupcakes for $2 each and cookies for $1.50 each. On Saturday, they sold 120 items total and made $210. How many cupcakes did they sell?

• Stem: Prices ($2, $1.50) and total items (120).
• Conditions: Total revenue ($210).
• Question: Number of cupcakes (c).
• Answer Choices: (A) 30 (B) 60 (C) 90 (D) 100

THE DECISION FRAMEWORK (6 Steps – 90 Seconds Max)

Step 1: Define Variables (10 sec)

• Assign a letter to the unknown in the question.
• "How many cupcakes?" → c = cupcakes.
• The other unknown gets a second variable.
• "Cookies" → k = cookies.

Step 2: Translate Words into Equations (20 sec)

• Total items: c + k = 120
• Total revenue: 2c + 1.5k = 210
• Pro tip: Write units next to variables (e.g., 2c = $2 × cupcakes).

Step 3: Solve One Equation for One Variable (20 sec)

• From c + k = 120, solve for k:
• k = 120 – c

Step 4: Substitute into the Second Equation (20 sec)

• Replace k in the revenue equation:
• 2c + 1.5(120 – c) = 210
• Simplify:
• 2c + 180 – 1.5c = 210
• 0.5c = 30
• c = 60

Step 5: Check Units and Logic (10 sec)

• c = 60 cupcakes.
• k = 120 – 60 = 60 cookies.
• Revenue check: 2(60) + 1.5(60) = 120 + 90 = 210 ✔️

Step 6: Match to Answer Choices (10 sec)

• c = 60 → Answer: (B) 60

Worked Examples

Example 1 – Straightforward

A taxi charges a $3 base fee plus $2 per mile. If a ride costs $19, how many miles was the trip?

Step 1: m = miles. Step 2: - Base fee: 3 - Per mile: 2m - Total: 3 + 2m = 19 Step 3: Solve for m: - 2m = 16 - m = 8 Step 4: Match to choices → (C) 8

Example 2 – Common Trap Version

A farmer has 50 animals: chickens and cows. Chickens have 2 legs; cows have 4. If there are 140 legs total, how many cows are there?

Trap: Students rush to c + k = 50 and 2c + 4k = 140, then solve correctly—but the real trap is in the answer choices: - (A) 10 (B) 20 (C) 30 (D) 40

Step 1: c = cows, k = chickens. Step 2: - c + k = 50 - 4c + 2k = 140 Step 3: Solve k = 50 – c. Step 4: Substitute: - 4c + 2(50 – c) = 140 - 4c + 100 – 2c = 140 - 2c = 40 - c = 20 Step 5: k = 30 → Legs check: 4(20) + 2(30) = 80 + 60 = 140 ✔️ Step 6: Answer: (B) 20

Why the trap works: Choice (C) 30 is k (chickens), not c (cows).

Example 3 – Hard Variant

A gym offers two membership plans. Plan A: $40/month + $5/class. Plan B: $20/month + $10/class. After how many classes do both plans cost the same?

Step 1: x = number of classes. Step 2: - Plan A: 40 + 5x - Plan B: 20 + 10x - Set equal: 40 + 5x = 20 + 10x Step 3: Solve: - 40 – 20 = 10x – 5x - 20 = 5x - x = 4 Step 4: Check: - Plan A: 40 + 5(4) = $60 - Plan B: 20 + 10(4) = $60 ✔️ Step 5: Answer: (B) 4

Hard variant twist: The question asks for when costs are equal, not which plan is cheaper.

WRONG ANSWER PATTERNS

Common Mistakes

TIME STRATEGY

• Target time: 90 seconds per question.
• Skip if: You can’t define variables in 10 seconds.
• Minimum work: Write two equations before solving.

BACKSOLVING AND SHORTCUTS

1. Plug in Answer Choices (Last Resort):
2. Start with (B) or (C). If too high/low, eliminate half the choices.

3. Example: For c + k = 120 and 2c + 1.5k = 210, test (B) 60:

   • k = 60 → 2(60) + 1.5(60) = 120 + 90 = 210 ✔️

4. Elimination First:

5. If c + k = 120, and c must be less than 120, eliminate (D) 100.

6. Avoid Decimals:

7. Multiply equations by 2 to eliminate decimals (e.g., 2c + 1.5k = 210 → 4c + 3k = 420).

1-Minute Recap

"Here’s the 60-second version: Every word problem is a two-equation system. Step 1: Define your variable—what’s the question asking for? Step 2: Translate the words into two equations. Step 3: Solve one equation for one variable. Step 4: Substitute into the second equation. Step 5: Check your answer by plugging back in. Step 6: Match to the choices. The trap isn’t the math—it’s rushing past Step 1. Slow down, define your variable, and the rest is just arithmetic. You’ve got this."

Final Note

Under timed conditions, discipline beats speed. Follow the framework exactly—no shortcuts until you’ve mastered the steps. Word problems are predictable; the GED repeats the same structures. Drill 10 of these, and you’ll recognize the patterns on test day.