Discounts, Markups, Tips & Sales Tax - Sixth Grade Mathematics

Applying percent operations to commercial transactions enables consumers to calculate discounts, sales tax, retailer markups, and restaurant tips with financial precision.

The Structure of Commercial Percent Calculations

Commercial transactions involve either a reduction in price (subtraction) or an addition to the price (addition).

+-------------------------------------------------------------------------+
|                  COMMERCIAL PERCENT CALCULATION STRUCTURE               |
+-------------------+-----------------------+-----------------------------+
| Transaction Type  | Nature of Change      | Governing Formula           |
+-------------------+-----------------------+-----------------------------+
| Discount / Sale   | DECREASE (-)          | Discount = Price * Rate     |
|                   | (Customer pays less)  | Sale Price = Price - Discnt |
+-------------------+-----------------------+-----------------------------+
| Sales Tax         | INCREASE (+)          | Tax = Price * Tax Rate      |
|                   | (Government levy)     | Total = Price + Tax         |
+-------------------+-----------------------+-----------------------------+
| Tip / Gratuity    | INCREASE (+)          | Tip = Bill * Tip Rate       |
|                   | (Service bonus)       | Total = Bill + Tip          |
+-------------------+-----------------------+-----------------------------+
| Retail Markup     | INCREASE (+)          | Markup = Cost * Markup Rate |
|                   | (Store profit margin) | Selling Price = Cost + Markup|
+-------------------+-----------------------+-----------------------------+

Calculating Discounts and Sale Prices

A discount is a reduction in the original price of an item.

Worked Example: A winter coat originally priced at $80 is on sale for 25% off.
What is the sale price?

Method 1 (Two-Step: Calculate Discount First):
Step 1: Calculate discount amount: 25% of $80 = 0.25 * 80 = $20 discount.
Step 2: Subtract discount from original price: $80 - $20 = $60 sale price.

Method 2 (One-Step: Complementary Percent):
If the discount is 25%, the customer pays 100% - 25% = 75% of the price!
Sale Price = 75% of $80 = 0.75 * 80 = $60.

The Power of Complementary Percents

Method 2 (using the complement) saves substantial time: A 30% discount means you pay 70% of the original price (Price * 0.70). A 15% discount means you pay 85% of the original price (Price * 0.85).

Calculating Sales Tax and Restaurant Tips

Sales tax and tips add to the cost of goods and services.

Worked Example: A meal costs $45.00. Sales tax is 8%, and the customer
leaves an 18% tip on the meal price. What is the total cost?

Step 1: Calculate Sales Tax:
        Tax = 8% of $45 = 0.08 * 45 = $3.60.

Step 2: Calculate Tip (based on meal subtotal):
        Tip = 18% of $45 = 0.18 * 45 = $8.10.

Step 3: Combine all components:
        Total = Meal ($45.00) + Tax ($3.60) + Tip ($8.10)
        Total = $56.70.

Retail Markups: Wholesale to Retail Price

Retail stores purchase inventory from manufacturers at wholesale cost and add a markup percentage so the store earns a profit when selling to customers. If a shoe store buys sneakers for $40 wholesale and marks them up by 60%: Markup amount = 60% of $40 = 0.60 * 40 = $24. Retail selling price = $40 wholesale + $24 markup = $64.

Exercises

Exercise 1. A skateboard originally costs $120. It is on sale for a 35% discount. Calculate the discount amount and the final sale price.

Exercise 2. A customer purchases a television for $450 in a city with an 8.5% sales tax rate. What is the sales tax amount, and what is the total cost at checkout?

Exercise 3. A furniture store buys a desk for $150 wholesale and applies a 45% markup. What is the selling price of the desk in the showroom?

Solutions

Solution to Exercise 1. Calculate the discount amount: 35% of $120 = 0.35 * 120 = $42.00. Subtract discount from original price: $120 - $42 = $78.00. The discount is $42.00, and the final sale price is $78.00.

Solution to Exercise 2. Calculate the sales tax amount: 8.5% of $450 = 0.085 * 450. Multiply: 450 * 0.085 = 38.25. The sales tax is $38.25. Add tax to purchase price: $450 + $38.25 = $488.25. The total cost at checkout is $488.25.

Solution to Exercise 3. Calculate the markup amount: 45% of $150 = 0.45 * 150 = $67.50. Add markup to wholesale cost: $150 + $67.50 = $217.50. The showroom selling price of the desk is $217.50.