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Percent Problems

Finding percent of a number, percent increase/decrease

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Percent Problems

Finding a Percent of a Number

Method: Convert percent to decimal, then multiply.

Example: What is 25% of 60? 0.25×60=150.25 \times 60 = 15

The Percent Equation

Part=Percent×Whole\text{Part} = \text{Percent} \times \text{Whole}

Can be rearranged:

  • Percent=PartWhole\text{Percent} = \frac{\text{Part}}{\text{Whole}}
  • Whole=PartPercent\text{Whole} = \frac{\text{Part}}{\text{Percent}}

Percent Increase

Percent Increase=New−OriginalOriginal×100%\text{Percent Increase} = \frac{\text{New} - \text{Original}}{\text{Original}} \times 100\%

Example: Price increases from \20toto$25$: 25−2020×100%=520×100%=25%\frac{25 - 20}{20} \times 100\% = \frac{5}{20} \times 100\% = 25\%

Percent Decrease

Percent Decrease=Original−NewOriginal×100%\text{Percent Decrease} = \frac{\text{Original} - \text{New}}{\text{Original}} \times 100\%

Example: Price drops from \40toto$30$: 40−3040×100%=1040×100%=25%\frac{40 - 30}{40} \times 100\% = \frac{10}{40} \times 100\% = 25\%

Tips and Discounts

Discount: amount saved Sale price = Original price - Discount

Tip/Tax: added amount Total = Original + Tip (or Tax)

Common Percent Problems

  • Finding a sale price: Original ×\times (1 - percent off)
  • Finding total with tax: Original ×\times (1 + tax rate)

📚 Practice Problems

1Problem 1easy

❓ Question:

What is 30% of 80?

💡 Show Solution

Convert percent to decimal and multiply:

30%=0.3030\% = 0.30

0.30×80=240.30 \times 80 = 24

Answer: 2424

2Problem 2medium

❓ Question:

A shirt costs \40$. It is on sale for 25% off. What is the sale price?

💡 Show Solution

Method 1: Find discount, then subtract Discount=0.25×40=10\text{Discount} = 0.25 \times 40 = 10 Sale price=40−10=30\text{Sale price} = 40 - 10 = 30

Method 2: Multiply by (1 - 0.25) Sale price=40×0.75=30\text{Sale price} = 40 \times 0.75 = 30

Answer: \30$

3Problem 3hard

❓ Question:

A population increased from 250 to 300. What is the percent increase?

💡 Show Solution

Use percent increase formula:

Percent Increase=New−OriginalOriginal×100%\text{Percent Increase} = \frac{\text{New} - \text{Original}}{\text{Original}} \times 100\%

=300−250250×100%= \frac{300 - 250}{250} \times 100\%

=50250×100%= \frac{50}{250} \times 100\%

=0.2×100%=20%= 0.2 \times 100\% = 20\%

Answer: 20% increase

4Problem 4medium

❓ Question:

A jacket originally costs $80. It goes on sale for 30% off. What is the sale price?

💡 Show Solution

Method 1: Find discount, then subtract Step 1: Find 30% of 80.0.30×80=80. 0.30 × 80 = 24 discount

Step 2: Subtract from original. 80−80 - 24 = $56

Method 2: Find what you pay directly Step 1: If 30% off, you pay 70%. 100% - 30% = 70%

Step 2: Find 70% of 80.0.70×80=80. 0.70 × 80 = 56

Answer: $56

5Problem 5hard

❓ Question:

You got 17 out of 20 questions correct on a test. What is your percentage score? Then, if the teacher adds 5 bonus points to your raw score, what is your new percentage?

💡 Show Solution

Part 1: Original percentage Step 1: Set up the fraction. 17/20

Step 2: Convert to decimal. 17 ÷ 20 = 0.85

Step 3: Convert to percent. 0.85 = 85%

Part 2: With bonus points Step 1: New score. 17 + 5 = 22 points earned Total still out of 20 (bonus goes above 100%)

Step 2: Calculate percent. 22/20 = 1.10 = 110%

Answer: Original: 85%, With bonus: 110%

Explain using:

⚠️ Common Mistakes: Percent Problems

Avoid these 3 frequent errors

🌍 Real-World Applications: Percent Problems

See how this math is used in the real world

📝 Worked Example: Solving a Quadratic by Factoring

Problem:

Solve x2−5x+6=0x^2 - 5x + 6 = 0.

2Factor the quadratic
3Set each factor equal to zero
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Solving Proportions
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📌 Related Topics in Ratios, Proportions, and Percents

Ratios and RatesSolving Proportions

❓ Frequently Asked Questions

What is Percent Problems?▾
Finding percent of a number, percent increase/decrease
How can I study Percent Problems effectively?▾
Start by reading the study notes and working through the examples on this page. Then use the flashcards to test your recall. Practice with the 5 problems provided, checking solutions as you go. Regular review and active practice are key to retention.
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Percent Problems is part of the Pre-Algebra course on Study Mondo, specifically in the Ratios, Proportions, and Percents section. You can explore the full course for more related topics and practice resources.
Are there practice problems for Percent Problems?▾
Yes, this page includes 5 practice problems with detailed solutions. Each problem includes a step-by-step explanation to help you understand the approach.