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Lesson 15

Multi-Step Real-World Challenges

Solve complex problems combining multiple percentage concepts.

  • expert

📚 Multi-Step Real-World Challenges

Congratulations on reaching the final lesson! These advanced problems combine multiple percentage concepts to solve complex real-world scenarios.

🎯 Challenge 1: Salary Negotiation

You earn $60,000. You negotiate an 8% raise, then receive a 5% bonus on your new salary. What's your total annual compensation?

1
New salary after 8% raise: $60,000 × 1.08 = $64,800
2
Bonus (5% of new salary): $64,800 × 0.05 = $3,240
3
Total compensation: $64,800 + $3,240 = $68,040

Note: The bonus is calculated on the NEW salary, not the original!

🎯 Challenge 2: Investment Portfolio

Your portfolio is 60% stocks, 30% bonds, and 10% cash. This year, stocks returned +12%, bonds +4%, and cash +1%. What's your total portfolio return?

1
Stocks contribution: 60% × 12% = 7.2%
2
Bonds contribution: 30% × 4% = 1.2%
3
Cash contribution: 10% × 1% = 0.1%
4
Total return: 7.2% + 1.2% + 0.1% = 8.5%

This is called a weighted average return!

💡 Expert Tips:

  • Always break complex problems into smaller steps
  • Be careful about order of operations - percentages don't always commute
  • Check if percentages are additive (like portfolio returns) or compound (like successive discounts)
  • Verify your answer makes intuitive sense

🎓 You've Mastered Percentages!

From basic concepts to expert-level challenges, you now have the skills to tackle any percentage problem. Keep practicing to maintain your expertise!

Frequently Asked Questions

How do I approach a multi-step percentage problem?

Name the base for each percentage, write the steps in order and compute them one at a time. A $200 item, 15% off, plus 8% tax, plus a 10% delivery fee on the taxed price is $200 × 0.85 × 1.08 × 1.10 = $201.96.

How can I check that a percentage answer makes sense?

Estimate first with round numbers, then check the direction: a discount must lower the price, tax must raise it, and a percentage of a whole must lie between zero and the whole.

Practice

Work each one out, then check yourself.

  1. Current salary $60,000, you get 8% raise, then 5% bonus on new salary. What's your total annual compensation?

    Hint: Step 1: $60,000 × 1.08 = $64,800. Step 2: Bonus = $64,800 × 0.05 = $3,240. Step 3: Total = $64,800 + $3,240

    Show answer

    67956

  2. Portfolio: 60% stocks (+12%), 30% bonds (+4%), 10% cash (+1%). What's the total return?

    Hint: Calculate weighted return: (0.60 × 12) + (0.30 × 4) + (0.10 × 1) = 7.2 + 1.2 + 0.1

    Show answer

    8.5

Final Quiz

0/3

Test what you learned. Pick the correct answer for each question.

  1. Item: 20% off then 10% off again. Combined discount?

    Item: 20% off then 10% off again. Combined discount?

  2. You earn 15% commission on a $5,000 sale. Tax takes 20% of commission. Take-home?

    You earn 15% commission on a $5,000 sale. Tax takes 20% of commission. Take-home?

  3. $2,000 invested at 6% compounded monthly for 2 years grows to approximately:

    $2,000 invested at 6% compounded monthly for 2 years grows to approximately: