How to Solve: Real-Life Math Problems

How to Solve: Real-Life Math Problems

Introduction

"Master this, and you’ll solve word problems on your exam—AND figure out real-life questions like ‘How much paint do I need for my room?’ or ‘Which phone plan saves me the most money?’ in seconds."

What You Need To Know First

Before tackling real-life math problems, you must already understand: 1. Basic arithmetic operations (addition, subtraction, multiplication, division). 2. Units of measurement (meters, liters, dollars, hours, etc.). 3. Simple equations (e.g., Total Cost = Price × Quantity).

If you’re shaky on any of these, review them first—this guide assumes you’re solid.

Key Vocabulary

Formulas To Know

Step-by-Step Method

Follow these 6 steps for every real-life math problem. No exceptions.

1. Read the problem twice.
2. First read: Get the general idea.

3. Second read: Underline numbers, units, and key words (e.g., "total," "per," "discount," "area").

4. Identify what’s being asked.

5. Circle the question (e.g., "How much will she pay?" or "What is the area?").

6. Write it as a blank: "She will pay _____ dollars."

7. List the given information.

8. Write each number with its unit (e.g., 5 kg, $12 per hour, 20% discount).

9. Label what each number means (e.g., $12 = hourly wage).

10. Choose the right formula.

11. Match the question to a formula from the list above.

12. If unsure, ask: "Is this about cost? Speed? Area?"

13. Plug in the numbers and solve.

14. Write the formula first, then substitute the numbers.

15. Show every step—examiners give partial credit!

16. Check your answer.

17. Does it make sense? (e.g., A $500 phone shouldn’t cost $5 after discount.)
18. Did you include the correct unit? (e.g., m² for area, $ for cost).

Worked Example Using the Steps

Problem: Liam wants to buy 4 notebooks. Each notebook costs $3.50. There’s a 10% discount on the total purchase. How much will Liam pay after the discount?

Step 1: Read twice. Underline key info: - 4 notebooks - $3.50 each - 10% discount - How much will Liam pay?

Step 2: What’s being asked? "Liam will pay _____ dollars after the discount."

Step 3: List given info: - Quantity = 4 notebooks - Price per notebook = $3.50 - Discount = 10%

Step 4: Choose formulas: 1. Total Cost = Price × Quantity 2. Discount Amount = Original Price × (Discount % ÷ 100) 3. Sale Price = Original Price – Discount Amount

Step 5: Solve step-by-step: 1. Total Cost = $3.50 × 4 = $14.00 2. Discount Amount = $14.00 × (10 ÷ 100) = $14.00 × 0.10 = $1.40 3. Sale Price = $14.00 – $1.40 = $12.60

Step 6: Check: - $12.60 is less than $14.00 (discount makes sense). - Units are in dollars (correct).

Final Answer: Liam will pay $12.60 after the discount.

Worked Examples

Example 1 - Basic: Buying Multiple Items

Problem: A pack of 6 pens costs $4.80. How much does one pen cost?

Solution: 1. What’s asked? "One pen costs _____ dollars." 2. Given: 6 pens = $4.80. 3. Formula: Price per pen = Total Cost ÷ Quantity 4. Solve: $4.80 ÷ 6 = $0.80 5. Check: $0.80 × 6 = $4.80 (correct).

What we did and why: We used division to find the unit rate (cost per pen). This is a common exam question—always divide total cost by quantity to find the price of one item.

Example 2 - Medium: Discounts and Tax

Problem: A jacket costs $80. There’s a 15% discount, and then a 5% sales tax is added to the discounted price. What’s the final price?

Solution: 1. What’s asked? "The final price is _____ dollars." 2. Given:
- Original price = $80
- Discount = 15%
- Tax = 5% 3. Formulas:
- Discount Amount = Original Price × (Discount % ÷ 100)
- Sale Price = Original Price – Discount Amount
- Tax Amount = Sale Price × (Tax % ÷ 100)
- Final Price = Sale Price + Tax Amount 4. Solve:
- Discount Amount = $80 × 0.15 = $12.00
- Sale Price = $80 – $12 = $68.00
- Tax Amount = $68 × 0.05 = $3.40
- Final Price = $68 + $3.40 = $71.40 5. Check:
- $71.40 is less than $80 (discount applied).
- Tax is added after discount (correct order).

What we did and why: We applied the discount first, then the tax. Examiners love testing if you know the order of operations—discounts reduce the price before tax is added.

Example 3 - Exam Style: Hidden Units

Problem: A rectangular garden is 12 meters long and 8 meters wide. Fencing costs $7 per meter. How much will it cost to fence the entire garden?

Solution: 1. What’s asked? "The cost to fence the garden is _____ dollars." 2. Given:
- Length = 12 m
- Width = 8 m
- Fencing cost = $7 per meter 3. Formulas:
- Perimeter = 2 × (Length + Width)
- Total Cost = Perimeter × Cost per meter 4. Solve:
- Perimeter = 2 × (12 + 8) = 2 × 20 = 40 meters
- Total Cost = 40 × $7 = $280 5. Check:
- Perimeter is in meters (correct unit).
- $280 is reasonable for 40 meters at $7/m.

What we did and why: We had to first find the perimeter (total fencing needed) before calculating cost. Examiners hide steps—always ask: "What do I need to find first?"

Common Mistakes

Exam Traps

1-Minute Recap

"Okay, let’s lock this in. Real-life math problems are just stories with numbers. Here’s how to crush them every time:

1. Read twice. Underline numbers, units, and key words like ‘per,’ ‘total,’ or ‘discount.’
2. Circle the question. What are you solving for? Write it as a blank.
3. List what you know. Every number + its meaning.
4. Pick the formula. Cost? Speed? Area? Match it to the question.
5. Solve step-by-step. Show your work—no shortcuts!
6. Check your answer. Does it make sense? Did you use the right units?

Common traps? ‘Per’ means divide, ‘total’ means multiply. Discounts come before tax. And if it’s about fencing or framing, it’s perimeter—not area.

You’ve got this. Now go ace that exam!

End of Guide