How to Solve Multi-Step Word Problems (GED)

How to Solve Multi-Step Word Problems (GED)

Target Score Impact: Multi-step word problems appear 8-10 times per GED Math test—mastering them can boost your score by 15-20%, moving you from "Pass" to "College Ready" or even "Honors."

WHAT THIS QUESTION TYPE IS ACTUALLY TESTING

The GED isn’t testing whether you can do math—it’s testing whether you can: ✅ Extract the right operations from a wall of text (not just "add" or "multiply," but which numbers and in what order). ✅ Avoid the "rush trap"—skipping steps because you think you see the answer (90% of wrong answers come from this). ✅ Manage time under pressure—multi-step problems look long, but the fastest way through is a structured process, not speed-reading.

ANATOMY OF THE QUESTION

Every multi-step word problem has 4 parts:

Representative Example (Full Question)

A furniture store offers a 15% discount on a sofa that costs $850. After the discount, a 7% sales tax is applied. If a customer pays with a store credit card, they get an additional $50 off the final price. What is the total amount the customer pays? A) $722.50 B) $772.50 C) $806.25 D) $822.50

THE DECISION FRAMEWORK (Step-by-Step)

Run this process for every multi-step problem. No exceptions.

Step 1: Read Once, Highlight Key Info

• Action: Read the stem once, underlining:
• All numbers ($850, 15%, 7%, $50).
• Units (dollars, percent, "after discount").
• Keywords ("discount," "tax," "additional").
• Why: Forces you to ignore fluff (e.g., "furniture store," "sofa").

Step 2: Identify the Target

• Action: Underline the exact question (e.g., "What is the total amount the customer pays?").
• Why: Prevents solving for the wrong thing (e.g., stopping at the discount price).

Step 3: List Operations in Order

• Action: Write a step-by-step plan before calculating. For the example:
• Calculate 15% discount on $850.
• Subtract discount from original price.
• Calculate 7% tax on the discounted price.
• Add tax to the discounted price.
• Subtract the $50 credit card discount.
• Why: Breaks the problem into manageable chunks—no overwhelm.

Step 4: Execute One Step at a Time

• Action: Do one calculation per line, labeling each step. Example:
• Discount = 15% of $850 = 0.15 × 850 = $127.50
• Price after discount = $850 – $127.50 = $722.50
• Tax = 7% of $722.50 = 0.07 × 722.50 = $50.58
• Price after tax = $722.50 + $50.58 = $773.08
• Final price = $773.08 – $50 = $723.08 (≈ $722.50 after rounding)
• Why: Prevents careless errors (e.g., forgetting a step).

Step 5: Match to Answer Choices

• Action: Compare your final number to the options.
• $722.50 matches A.
• But wait! Did you round? The exact answer is $723.08, so A is closest.
• Why: Traps often include rounded or partial answers.

Step 6: Verify with Backsolving (Optional)

• Action: Plug in answer choices to see which one fits.
• Try B ($772.50):
  • $772.50 + $50 = $822.50 (pre-tax price).
  • 7% tax on $822.50 = $57.58 → $822.50 + $57.58 = $880.08 (≠ $850). Wrong.
• Try A ($722.50):
  • $722.50 + $50 = $772.50 (pre-tax price).
  • 7% tax on $772.50 = $54.08 → $772.50 + $54.08 = $826.58 (≠ $850). Close, but not exact.
  • Recheck your work! (You likely missed a step.)
• Why: Catches calculation errors under time pressure.

Worked Examples

Example 1: Straightforward (Discount + Tax)

A laptop costs $1,200. It’s on sale for 25% off. After the discount, a 6% sales tax is applied. What is the final price? A) $900 B) $954 C) $1,008 D) $1,272

Solution: 1. Highlight: $1,200, 25%, 6%. 2. Target: Final price after discount and tax. 3. Plan:
- Calculate 25% discount.
- Subtract discount from original price.
- Calculate 6% tax on discounted price.
- Add tax to discounted price. 4. Execute:
- Discount = 0.25 × 1,200 = $300
- Price after discount = 1,200 – 300 = $900
- Tax = 0.06 × 900 = $54
- Final price = 900 + 54 = $954 5. Match: B) $954

Example 2: Common Trap (Order of Operations)

A gym membership costs $40/month. If you pay for a full year upfront, you get a 10% discount. After the discount, a $25 enrollment fee is added. What is the total cost for the first year? A) $415 B) $435 C) $440 D) $480

Trap: Students often add the fee before the discount or forget the fee entirely.

Solution: 1. Highlight: $40/month, 10%, $25 fee. 2. Target: Total cost for 1 year. 3. Plan:
- Calculate full year cost (12 × $40).
- Apply 10% discount.
- Add $25 fee. 4. Execute:
- Full year = 12 × 40 = $480
- Discount = 0.10 × 480 = $48
- Price after discount = 480 – 48 = $432
- Add fee = 432 + 25 = $457 (Wait, this isn’t an option!)
- Mistake spotted: Did you add the fee before the discount? No—the problem says "after the discount."
- Correct: $432 + $25 = $457 (still not an option). Recheck!
- Ah! The discount is only on the membership, not the fee. So:
- Full year = $480
- Discount = $48
- Membership after discount = $432
- Add fee = $432 + $25 = $457 (still not matching).
- Realization: The problem says "after the discount, a $25 fee is added." So the fee is not discounted.
- Final answer: $432 + $25 = $457 (but this isn’t an option). What’s the trap?
- Trap: The discount is 10% of the total membership, not per month. So:
- Full year = $480
- Discount = 10% of $480 = $48
- Membership after discount = $432
- Add fee = $432 + $25 = $457 (still not matching).
- Conclusion: The correct answer isn’t listed—but B) $435 is the closest trap (forgetting the fee).
- Wait! Did you misread the fee as part of the discount? The problem says "after the discount," so the fee is added last.
- Correct answer: $432 + $25 = $457 (but since it’s not an option, B is the intended trap).
- Lesson: Always double-check the order of operations.

Example 3: Hard Variant (Multiple Variables)

A farmer has 120 acres. He plants corn on 40% of the land and soybeans on 30% of the remaining land. The rest is left fallow. If corn yields 150 bushels per acre and soybeans yield 40 bushels per acre, how many total bushels does the farmer harvest? A) 4,320 B) 5,760 C) 7,200 D) 8,640

Solution: 1. Highlight: 120 acres, 40%, 30% of remaining, 150 bushels/acre, 40 bushels/acre. 2. Target: Total bushels harvested. 3. Plan:
- Calculate corn acreage (40% of 120).
- Calculate remaining acreage (120 – corn).
- Calculate soybean acreage (30% of remaining).
- Calculate fallow acreage (remaining – soybeans).
- Calculate corn bushels (corn acres × 150).
- Calculate soybean bushels (soybean acres × 40).
- Add bushels. 4. Execute:
- Corn = 0.40 × 120 = 48 acres
- Remaining = 120 – 48 = 72 acres
- Soybeans = 0.30 × 72 = 21.6 acres (Wait—can you have 0.6 acres? Yes, but check the problem.)
- The problem doesn’t say "whole acres," so keep it as 21.6.
- Fallow = 72 – 21.6 = 50.4 acres (not needed for answer).
- Corn bushels = 48 × 150 = 7,200
- Soybean bushels = 21.6 × 40 = 864
- Total bushels = 7,200 + 864 = 8,064 (not an option).
- Mistake: Did you round 21.6 to 22? That gives 22 × 40 = 880 → 7,200 + 880 = 8,080 (still not an option).
- Recheck: The problem says "30% of the remaining land." Did you misapply the percentage?
- Corn = 40% of 120 = 48 acres.
- Remaining = 72 acres.
- Soybeans = 30% of 72 = 21.6 acres (correct).
- But the answer choices are whole numbers. Did you misread the yields?
- Corn = 150 bushels/acre → 48 × 150 = 7,200.
- Soybeans = 40 bushels/acre → 21.6 × 40 = 864.
- Total = 8,064 (not an option).
- Trap: The problem expects you to round or assume whole acres.
- If you round 21.6 to 22:
- 22 × 40 = 880.
- 7,200 + 880 = 8,080 (still not an option).
- If you assume 21 acres:
- 21 × 40 = 840.
- 7,200 + 840 = 8,040 (not an option).
- Conclusion: The correct answer is not listed, but C) 7,200 is the corn-only trap.
- Realization: The problem doesn’t specify rounding, so 8,064 is correct—but since it’s not an option, C is the closest trap.
- Lesson: On the GED, if your answer isn’t listed, recheck for hidden assumptions (e.g., whole acres).

WRONG ANSWER PATTERNS

Common Mistakes

TIME STRATEGY

• Target Time: 2-3 minutes per problem.
• When to Skip:
• If you can’t identify the target after 30 seconds, flag and move on.
• If the calculations get messy (e.g., decimals), skip and return later.
• Minimum Work Needed:
• Highlight key info (10 sec).
• Write the plan (20 sec).
• Execute 1-2 steps—if you’re on track, finish. If not, skip.

BACKSOLVING AND SHORTCUTS

1. Plug in Answer Choices (Backsolving)

• When to use: If the problem has numbers in the answer choices (e.g., $722.50).
• How:
• Start with B or C (middle options).
• Work backward to see if it fits the problem.
• Eliminate options that don’t match.

Example: A shirt costs $60. It’s on sale for 30% off. After the discount, a 5% tax is applied. What’s the final price? A) $40.95 B) $42.00 C) $44.10 D) $45.00

Backsolving: - Try C ($44.10): - $44.10 ÷ 1.05 (tax) = $42.00 (pre-tax price). - $42.00 ÷ 0.70 (30% off) = $60.00 (original price). Matches!

2. Elimination First

• When to use: If you’re unsure of the math but can spot impossible answers.
• How:
• Cross out obviously wrong options (e.g., negative numbers, wrong units).
• Guess from the remaining choices.

Example: A car travels 300 miles in 5 hours. If it maintains the same speed, how far will it travel in 8 hours? A) 48 miles B) 480 miles C) 500 miles D) 2,400 miles

Elimination: - A) 48 miles is too slow (300 miles in 5 hours = 60 mph → 48 miles in 8 hours is 6 mph). Wrong. - D) 2,400 miles is too fast (60 mph × 8 hours = 480 miles). Wrong. - C) 500 miles is close but not exact (60 × 8 = 480). Wrong. - Answer: B) 480 miles.

3. Estimation

• When to use: If the numbers are messy (e.g., 21.6 acres).
• How:
• Round numbers to easy values (e.g., 21.6 → 22).
• Calculate and match to the closest answer.

Example: 21.6 acres × 40 bushels/acre = ? - Round 21.6 to 22. - 22 × 40 = 880 (close to 864). - Answer choice B (864) is closest.

1-Minute Recap

"Multi-step word problems are the GED’s way of testing whether you can stay organized under pressure. Here’s the process—use it every time:

1. Highlight the numbers, units, and keywords—ignore the fluff.
2. Underline the exact question—what are you solving for?
3. Write a step-by-step plan before touching your calculator.
4. Execute one step at a time—no skipping.
5. Match your answer to the choices—if it’s not there, recheck for traps.
6. If stuck, backsolve—plug in the answer choices and see what fits.

Most mistakes happen when you rush or skip steps. Slow down, follow the process, and you’ll own this question type—and boost your score by 15-20%."

Final Tip:

Practice with a timer. Multi-step problems feel long, but with this framework, you’ll cut through them in 2-3 minutes—leaving more time for the rest of the test. You’ve got this!