Discounts, Taxes, and Profit

Learn how to calculate discounts, add taxes, and compute profit. Understand the formulas and apply them to everyday shopping and sales problems.

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How to use this guide

This guide will teach you how to calculate discounts, add taxes, and find profit. Work through each section and apply the formulas to the practice problems.

Big idea: Discounts reduce the original price, taxes increase the price, and profit is the difference between selling and buying prices.

Calculating Discounts

To find a discount:

\[ \text{Discount Amount} = \frac{\text{Discount %}}{100} \times \text{Original Price} \] \[ \text{Price After Discount} = \text{Original Price} - \text{Discount Amount} \]

Example: Find the discount on an item priced at $120 with a 15% discount.

\[ \text{Discount Amount} = \frac{15}{100} \times 120 = 18 \] \[ \text{Price After Discount} = 120 - 18 = 102 \]

Adding Taxes

To add sales tax:

\[ \text{Tax Amount} = \frac{\text{Tax %}}{100} \times \text{Original Price} \] \[ \text{Total Price} = \text{Original Price} + \text{Tax Amount} \]

Example: Calculate the total price after adding 8% sales tax to $250.

\[ \text{Tax Amount} = \frac{8}{100} \times 250 = 20 \] \[ \text{Total Price} = 250 + 20 = 270 \]

Profit Calculation

To calculate profit:

\[ \text{Profit} = \text{Selling Price} - \text{Cost Price} \]

Example: A shirt was bought for $40 and sold for $55. What is the profit?

\[ \text{Profit} = 55 - 40 = 15 \]

Example Problems

Problem 1: A TV costs $500 with a 10% discount. Find the price after discount.

\[ \text{Discount Amount} = \frac{10}{100} \times 500 = 50 \] \[ \text{Price After Discount} = 500 - 50 = 450 \]

Problem 2: Add 12% tax to $600 purchase. Find total cost.

\[ \text{Tax Amount} = \frac{12}{100} \times 600 = 72 \] \[ \text{Total Price} = 600 + 72 = 672 \]

Problem 3: A book bought for $30 is sold for $45. Find profit.

\[ \text{Profit} = 45 - 30 = 15 \]

Mixed Practice

Problem 1: An item costs $200 with a 20% discount. Find the discounted price.

\[ \text{Discount Amount} = \frac{20}{100} \times 200 = 40 \] \[ \text{Price After Discount} = 200 - 40 = 160 \]

Problem 2: Add 15% tax to a $120 purchase. Find total price.

\[ \text{Tax Amount} = \frac{15}{100} \times 120 = 18 \] \[ \text{Total Price} = 120 + 18 = 138 \]

Problem 3: Bought a gadget for $80 and sold for $100. Find the profit.

\[ \text{Profit} = 100 - 80 = 20 \]

Test