Solved Exercises on Sales Tax and Tips in Grade 7

Master sales tax and tips: calculating tax amounts, tip percentages, total costs, and real-world financial scenarios through these 10 detailed exercises with visual learning tools.

Solution: Exercises 1 to 3
1 Basic Sales Tax Calculation
Exercise 1
A jacket costs $80. If the sales tax rate is 8%, what is the total cost including tax?
Definition:

Sales tax: A percentage added to the purchase price that is collected by the seller and remitted to the government.

Method:
  1. Calculate the tax amount by multiplying the price by the tax rate
  2. Add the tax amount to the original price
  3. Express the total as the final answer
Step 1: Calculate the tax amount

Tax amount = $80 × 0.08 = $6.40

Step 2: Calculate the total cost

Total cost = $80 + $6.40 = $86.40

Step 3: State the final answer

The total cost including tax is $86.40

Original price:
$80.00
Sales tax (8%):
$6.40
Total:
$86.40
Total cost: $86.40
Final answer:

The total cost of the jacket including 8% sales tax is $86.40.

Applied rules:

• Percent to decimal: 8% = 0.08

• Tax calculation: Price × Tax rate

• Total cost: Original price + Tax amount

2 Tip Calculation
Exercise 2
A restaurant bill is $45. If you want to leave a 15% tip, how much should the tip be? What is the total amount paid?
Definition:

Tip: A percentage-based gratuity added to a service bill as a reward for good service.

Step 1: Calculate the tip amount

Tip amount = $45 × 0.15 = $6.75

Step 2: Calculate the total amount paid

Total amount = $45 + $6.75 = $51.75

Step 3: State the answers

Tip: $6.75, Total: $51.75

Bill amount:
$45.00
Tip (15%):
$6.75
Total:
$51.75
Tip: $6.75, Total: $51.75
Final answer:

The tip amount is $6.75, and the total amount paid is $51.75.

Applied rules:

• Percent to decimal: 15% = 0.15

• Tip calculation: Bill × Tip percentage

• Total payment: Bill + Tip

3 Combined Tax and Tip
Exercise 3
A meal costs $60 before tax. If the sales tax rate is 7% and you want to leave a 20% tip on the pre-tax amount, what is the total amount paid?
Definition:

Combined calculation: When both tax and tip are added to the original amount, calculate each separately.

Step 1: Calculate the sales tax

Tax = $60 × 0.07 = $4.20

Step 2: Calculate the tip on pre-tax amount

Tip = $60 × 0.20 = $12.00

Step 3: Calculate the total amount

Total = $60 + $4.20 + $12.00 = $76.20

Pre-tax amount:
$60.00
Sales tax (7%):
$4.20
Tip (20%):
$12.00
Total:
$76.20
Total amount: $76.20
Final answer:

The total amount paid is $76.20.

Applied rules:

• Separate calculations: Calculate tax and tip separately

• Tip base: Tip is calculated on the pre-tax amount

• Total calculation: Original + Tax + Tip

Solution: Exercises 4 to 6
4 Finding Tax Rate
Exercise 4
An item costs $25 before tax and $26.50 after tax. What is the sales tax rate?
Definition:

Finding tax rate: When the tax amount and original price are known, calculate the percentage rate.

Step 1: Calculate the tax amount

Tax amount = $26.50 - $25 = $1.50

Step 2: Calculate the tax rate

Tax rate = ($1.50 ÷ $25) × 100 = 0.06 × 100 = 6%

Step 3: Verify the answer

$25 × 0.06 = $1.50, $25 + $1.50 = $26.50 ✓

Pre-tax price:
$25.00
Post-tax price:
$26.50
Tax amount:
$1.50
Tax rate:
6%
Tax rate: 6%
Final answer:

The sales tax rate is 6%.

Applied rules:

• Tax amount: Post-tax - Pre-tax

• Tax rate: (Tax amount ÷ Pre-tax) × 100

• Verification: Multiply pre-tax by rate to confirm tax amount

5 Reverse Tax Calculation
Exercise 5
A purchase costs $105 after a 5% sales tax is added. What was the original price before tax?
Definition:

Reverse calculation: Finding the original amount when the final amount and percentage are known.

Step 1: Set up the equation

If original price is P, then P + (0.05 × P) = $105

Step 2: Simplify the equation

P(1 + 0.05) = $105, so 1.05P = $105

Step 3: Solve for P

P = $105 ÷ 1.05 = $100

Step 4: Verify the answer

$100 + (5% of $100) = $100 + $5 = $105 ✓

Final price:
$105.00
Tax rate:
5%
Original price:
$100.00
Tax amount:
$5.00
Original price: $100
Final answer:

The original price before tax was $100.

Applied rules:

• Reverse calculation: Final amount ÷ (1 + tax rate)

• Algebraic equation: Set up equation with unknown variable

• Verification: Check answer by calculating forward

6 Tip Percentage Calculation
Exercise 6
You leave a $12 tip on a $80 restaurant bill. What percentage tip did you leave?
Definition:

Tip percentage: The percentage of the bill amount that was left as a tip.

Step 1: Calculate the tip percentage

Tip percentage = ($12 ÷ $80) × 100 = 0.15 × 100 = 15%

Step 2: Verify the calculation

15% of $80 = 0.15 × $80 = $12 ✓

Step 3: State the answer

You left a 15% tip

Bill amount:
$80.00
Tip amount:
$12.00
Tip percentage:
15%
Tip percentage: 15%
Final answer:

You left a 15% tip on the restaurant bill.

Applied rules:

• Percentage calculation: (Part ÷ Whole) × 100

• Tip percentage: (Tip amount ÷ Bill amount) × 100

• Verification: Calculate tip from percentage to confirm

Sales Tax and Tips Visual Guide
Tax = Price × Rate, Tip = Bill × Rate
Key Formulas
Sales Tax
Government fee
Tips
Service gratuity
Percent
Decimal conversion
Calculation
Multiply & add
Calculation Process:
Step 1: Convert percentage to decimal (divide by 100)
Step 2: Multiply original amount by decimal rate
Step 3: Add tax/tip to original amount for total
Step 4: Verify calculation makes sense
Tip 1: Remember: 8% = 0.08, 15% = 0.15, 20% = 0.20
Tip 2: Always calculate tax before adding tip if tip is on pre-tax amount
Tip 3: Round to nearest cent for currency amounts
Common errors: Forgetting to convert percentage to decimal, calculating tax on post-tax amount.
Success strategies: Check reasonableness of answers, verify calculations.
Essential concepts:

• Tax: Added to purchase price

• Tip: Added to service bill

• Percent to decimal: Divide by 100

• Total: Original + Tax + Tip

Solution: Exercises 7 to 10
7 Multiple Item Purchase
Exercise 7
Sarah buys 3 shirts at $25 each and 2 pairs of jeans at $40 each. If the sales tax rate is 6%, what is the total cost?
Definition:

Multiple item purchase: Calculating tax on the total cost of all items.

Step 1: Calculate the cost of shirts

3 × $25 = $75

Step 2: Calculate the cost of jeans

2 × $40 = $80

Step 3: Calculate the subtotal

$75 + $80 = $155

Step 4: Calculate the tax

$155 × 0.06 = $9.30

Step 5: Calculate the total cost

$155 + $9.30 = $164.30

Shirts (3 × $25):
$75.00
Jeans (2 × $40):
$80.00
Subtotal:
$155.00
Tax (6%):
$9.30
Total:
$164.30
Total cost: $164.30
Final answer:

The total cost including tax is $164.30.

Applied rules:

• Subtotal first: Calculate total before tax

• Single tax rate: Apply tax to entire subtotal

• Final total: Subtotal + Tax

8 Restaurant Scenario
Exercise 8
A dinner bill is $120 before tax. The sales tax is 8%, and you want to leave a 18% tip on the post-tax amount. What is the total amount paid?
Definition:

Post-tax tip: When tip is calculated on the amount including tax.

Step 1: Calculate the sales tax

$120 × 0.08 = $9.60

Step 2: Calculate the post-tax amount

$120 + $9.60 = $129.60

Step 3: Calculate the tip

$129.60 × 0.18 = $23.33

Step 4: Calculate the total amount

$129.60 + $23.33 = $152.93

Pre-tax bill:
$120.00
Tax (8%):
$9.60
Post-tax amount:
$129.60
Tip (18%):
$23.33
Total:
$152.93
Total amount: $152.93
Final answer:

The total amount paid is $152.93.

Applied rules:

• Post-tax tip: Tip is calculated on amount including tax

• Sequential calculation: Tax first, then tip

• Final total: Original + Tax + Tip

9 Sale with Tax
Exercise 9
A $150 item is on sale for 20% off. If the sales tax rate is 7%, what is the final cost?
Definition:

Sale with tax: Calculate discount first, then apply tax to the discounted price.

Step 1: Calculate the discount amount

$150 × 0.20 = $30

Step 2: Calculate the discounted price

$150 - $30 = $120

Step 3: Calculate the sales tax

$120 × 0.07 = $8.40

Step 4: Calculate the final cost

$120 + $8.40 = $128.40

Original price:
$150.00
Discount (20%):
$30.00
Discounted price:
$120.00
Tax (7%):
$8.40
Final cost:
$128.40
Final cost: $128.40
Final answer:

The final cost after discount and tax is $128.40.

Applied rules:

• Discount first: Calculate discount on original price

• Tax on discounted: Apply tax to discounted price

• Final cost: Discounted price + Tax

10 Budget Planning
Exercise 10
You have $100 to spend at a store where the sales tax rate is 5%. What is the maximum amount you can spend before tax?
Definition:

Budget planning: Finding the maximum pre-tax amount when total budget and tax rate are known.

Step 1: Set up the equation

If P is the pre-tax amount, then P + (0.05 × P) = $100

Step 2: Simplify the equation

P(1 + 0.05) = $100, so 1.05P = $100

Step 3: Solve for P

P = $100 ÷ 1.05 = $95.24

Step 4: Verify the answer

$95.24 + (5% of $95.24) = $95.24 + $4.76 = $100.00 ✓

Total budget:
$100.00
Tax rate:
5%
Max pre-tax:
$95.24
Tax amount:
$4.76
Maximum pre-tax: $95.24
Final answer:

You can spend a maximum of $95.24 before tax.

Applied rules:

• Budget equation: Pre-tax + Tax = Total budget

• Algebraic solution: Solve for unknown pre-tax amount

• Verification: Confirm total equals budget

Comprehensive Summary: Sales Tax and Tips
Core Concepts & Definitions:

Sales Tax: A percentage-based fee imposed by the government on goods and services.

Tip: A voluntary percentage-based payment added to service bills as appreciation for good service.

Percent: A ratio expressed as a fraction of 100 (e.g., 8% = 8/100 = 0.08).

Pre-tax Amount: The original price before tax is added.

Post-tax Amount: The price after tax has been added.

Discount: A reduction in the original price.

Final Cost: The total amount paid after all taxes, tips, and discounts.

Core Rules & Formulas:

Essential Formulas:

  • Sales tax amount = Price × Tax rate (as decimal)
  • Tip amount = Bill amount × Tip rate (as decimal)
  • Total cost = Original price + Tax + Tip
  • Tax rate = (Tax amount ÷ Original price) × 100
  • Original price = Final amount ÷ (1 + Tax rate)

Key Rules:

  • Always convert percentages to decimals before calculating
  • Calculate tax before adding tip if tip is on pre-tax amount
  • Round monetary amounts to the nearest cent
Step-by-Step Calculation Process:
  1. Convert percentage: Change percentage to decimal (divide by 100)
  2. Calculate tax/tip: Multiply original amount by decimal rate
  3. Add to original: Add tax or tip to the original amount
  4. Verify calculation: Check that your answer makes sense
Examples & Applications:

Simple Tax Example:

  • Item costs $50, tax rate is 6%
  • Tax = $50 × 0.06 = $3
  • Total = $50 + $3 = $53

Simple Tip Example:

  • Bill is $80, tip rate is 18%
  • Tip = $80 × 0.18 = $14.40
  • Total = $80 + $14.40 = $94.40

Combined Example:

  • Meal costs $60, tax is 7%, tip is 15%
  • Tax = $60 × 0.07 = $4.20
  • Tip = $60 × 0.15 = $9.00
  • Total = $60 + $4.20 + $9.00 = $73.20
Tips, Tricks & Common Mistakes:

Tips & Tricks:

  • Memorize common percentage conversions: 10% = 0.10, 15% = 0.15, 20% = 0.20
  • Estimate first to check if your answer is reasonable
  • Always round monetary amounts to two decimal places
  • Remember that tip is usually calculated on pre-tax amount unless specified otherwise

Common Mistakes:

  • Forgetting to convert percentages to decimals
  • Calculating tax on the post-tax amount
  • Adding tax and tip percentages together before calculating
  • Miscalculating when dealing with multiple items
Key Notes for Memorization:
  • Percent to decimal: Divide by 100
  • Tax = Original × Rate
  • Tip = Bill × Rate
  • Total = Original + Tax + Tip
  • Always calculate tax before tip (unless specified otherwise)
  • Round to nearest cent for money
Additional Sales Tax and Tips Practice
Tax = Price × Rate, Total = Original + Tax
Key Formulas
Key definitions:

Sales tax: Government-imposed fee on purchases

Tips: Voluntary gratuities for services

Percentages: Ratios expressed per hundred

Calculation methodology:
  1. Convert: Change percentage to decimal
  2. Multiply: Calculate tax or tip amount
  3. Add: Include in total cost
  4. Verify: Check answer for reasonableness
Tip 1: Always include units (dollars) in your final answer.
Tip 2: Use estimation to check if your answer is reasonable.
Tip 3: Round monetary amounts to the nearest cent.
Tip 4: Remember to calculate tax before adding tip.
Common errors: Forgetting decimal conversion, wrong order of operations, calculation mistakes.
Success strategies: Systematic approach, verification, proper rounding.
Essential concepts:

• Tax: Add to original price

• Tip: Add to service bill

• Percent: Divide by 100

• Total: Sum of all amounts

Questions & Answers

Question: When do I calculate tax first versus tip first? Does the order matter?

Answer: The order matters depending on what the tip is based on:

  • If tip is on pre-tax amount: Calculate tax first, then add tip to the original amount
  • If tip is on post-tax amount: Calculate tax first, add to get post-tax amount, then calculate tip on that total

In most real-world situations, tip is calculated on the pre-tax amount, so tax comes first.

Question: How do I quickly convert percentages to decimals? It's hard to remember.

Answer: Use this memory trick: Move the decimal point two places to the left:

  • 5% → 0.05 (decimal moves two places left)
  • 12% → 0.12
  • 25% → 0.25
  • 100% → 1.00

Think of it as dividing by 100, which moves the decimal point two positions to the left.

Question: What's the difference between calculating tax backward (finding original price) versus forward (finding total)?

Answer: The direction determines the operation:

  • Forward (original → total): Multiply by (1 + tax rate)
  • Backward (total → original): Divide by (1 + tax rate)

For example: $100 with 5% tax → $100 × 1.05 = $105. From $105 back to original → $105 ÷ 1.05 = $100.