Fractions, Decimals & Percents (Mastery) • Topic 1 of 3

Percent Word Problems - Discounts, Tax, Tips

Percent Review:

Percent means "out of 100." To find a percent of a number:

Convert percent to decimal (divide by 100)
Multiply by the number

Types of Percent Problems:

Type	Formula	Example
Discount	Original × (Percent off) = Savings	20% off 50 =10 saved
Sale Price	Original - Savings	50 -10 = 40 \| \| Tax \| Price × Tax rate = Tax amount \|40 × 0.08 = 3.20 tax \| \| Tip \| Bill × Tip rate = Tip amount \|50 × 0.15 = 7.50 tip \| \| Total with tax/tip \| Price + Tax/Tip \|40 + 3.20 =43.20
Percent Increase	(New - Original)/Original × 100	(60-50)/50 = 20%
Percent Decrease	(Original - New)/Original × 100	(50-40)/50 = 20%

DISCOUNT CALCULATION - BAR MODEL:

 Original Price: 80 (100%)
 
 ┌───────────────┬───────────────┐
 │ 25% OFF │ 75% PAY │
 │ (20 saved) │ (60) │
 └───────────────┴───────────────┘
 
 Step 1: 25% of 80 = 0.25 × 80 = 20 saved
 Step 2: Sale price = 80 - 20 = 60
 OR: Sale price = 75% of 80 = 0.75 × 80 = 60


TAX CALCULATION:

 Item price: 45
 Tax rate: 8%
 
 ┌─────────────────────────────────┐
 │ │
 │ 45.00 (item) │
 │ + 3.60 (tax = 45 × 0.08) │
 │ ───────────────────────── │
 │ 48.60 (total) │
 │ │
 └─────────────────────────────────┘


TIP CALCULATION:

 Restaurant bill: 35
 Tip rate: 18%
 
 Method 1: 35 × 0.18 = 6.30 tip
 Method 2: 10% = 3.50, 5% = 1.75, 
 3% = 1.05 → Total = 6.30
 
 Total bill = 35 + 6.30 = 41.30


PERCENT CHANGE FORMULA:

 Percent Change = (New - Original) / Original × 100
 
 Increase: Price 50 → 65
 (65 - 50)/50 × 100 = 15/50 × 100 = 30% increase
 
 Decrease: Price 50 → 35
 (35 - 50)/50 × 100 = -15/50 × 100 = -30% decrease
 (or 30% decrease)

Solved Examples

Worked Example

A 120 jacket is on sale for 30% off. What is the sale price?

Solution

Discount = 30% of 120 = 0.30 × 120 = 36
Sale price = 120 - 36 = 84
OR: Sale price = 70% of 120 = 0.70 × 120 = 84
Answer: 84

Worked Example

A meal costs 45. You want to leave a 15% tip. How much total will you pay?

Solution

Tip = 15% of 45 = 0.15 × 45 = 6.75
Total = 45 + 6.75 = 51.75
Answer: 51.75

Worked Example

You buy a 60 item with 7% sales tax. What is the total?

Solution

Tax = 7% of 60 = 0.07 × 60 = 4.20
Total = 60 + 4.20 = 64.20
Answer: 64.20

Worked Example

A population grew from 200 to 250. What is the percent increase?

Solution

Increase = 250 - 200 = 50
Percent = (50 ÷ 200) × 100 = 0.25 × 100 = 25%
Answer: 25% increase

Key Points

Discount = percent off × original price
Sale price = original - discount
Tax/tip = rate × price
Total = price + tax/tip
Percent change = (change ÷ original) × 100
To find original price: divide sale price by (1 - discount%)

Quick Check — 4 MCQs

Tap an option to check your answer0 / 4

Q1.$10\%$ of $200$ is:

Explanation: $\tfrac{10}{100}\times200$.

Q2.A discount ___ the price.

Explanation: Reduces.

Q3.Tax ___ the amount paid.

Explanation: Adds to it.

Q4.A tip is an extra amount added for:

Explanation: Service.

Practice more MCQs → 📝 Assignment · 35 marks