Percent Applications

Solve real-world problems involving discounts, tax, tips, and percent change

Percent Applications

Finding a Percent of a Number

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

Example: Find 25% of 80 $0.25 \times 80 = 20$

Percent Change

$\text{Percent Change} = \frac{\text{New - Original}}{\text{Original}} \times 100\%$

Positive = Increase
Negative = Decrease

Common Applications

Discount

Original price $\times$ (1 - discount rate)

Example: 20% off $\$ 50 $$$50 \times (1 - 0.20) = 50 \times 0.80 = \$ 40$$

Tax

Price $\times$ (1 + tax rate)

Example: $\$ 30 $with 8% tax $$30 \times 1.08 = \$ 32.40$$

Tip

Bill $\times$ tip rate

Example: 15% tip on $\$ 40 $$$40 \times 0.15 = \$ 6$$

📚 Practice Problems

1Problem 1easy

❓ Question:

A shirt costs $\$ 25$. It is on sale for 30% off. What is the sale price?

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Solution:

Method 1 - Find discount: $\text{Discount} = 0.30 \times 25 = \$7.50$ $\text{Sale price} = 25 - 7.50 = \$17.50$

Method 2 - Multiply by remaining percent: $25 \times (1 - 0.30) = 25 \times 0.70 = \$17.50$

Answer: $\$ 17.50$

2Problem 2medium

❓ Question:

A population increased from 15,000 to 18,000. What is the percent increase?

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Solution:

Use percent change formula: $\text{Percent Change} = \frac{18000 - 15000}{15000} \times 100\%$

$= \frac{3000}{15000} \times 100\%$

$= 0.2 \times 100\% = 20\%$

Answer: 20% increase

3Problem 3hard

❓ Question:

A meal costs $\$ 45$. You want to leave a 18% tip and there is 7% sales tax. What is the total amount you pay?

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Solution:

Step 1: Add tax to the meal $45 \times 1.07 = \$48.15$

Step 2: Calculate tip (on original meal) $45 \times 0.18 = \$8.10$

Step 3: Total $48.15 + 8.10 = \$56.25$

Answer: $\$ 56.25$

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