Percent Problems

Finding a Percent of a Number

Method: Convert percent to decimal, then multiply.

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

The Percent Equation

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

Can be rearranged:

• $\text{Percent} = \frac{\text{Part}}{\text{Whole}}$
• $\text{Whole} = \frac{\text{Part}}{\text{Percent}}$

Percent Increase

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

Example: Price increases from \20$to$$25$: $\frac{25 - 20}{20} \times 100\% = \frac{5}{20} \times 100\% = 25\%$

Percent Decrease

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

Example: Price drops from \40$to$$30$: $\frac{40 - 30}{40} \times 100\% = \frac{10}{40} \times 100\% = 25\%$

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)