6.3 Solve Sales Tax, Commission, and Discount Applications

Sales Tax, Commission, and Discounts

Sales tax, commission, and discounts all work the same way at their core: you're finding a percent of a number, then either adding it to or subtracting it from a price. Once you see that pattern, every problem in this section follows the same basic steps.

Sales Tax Calculations

Sales tax is a percentage that gets added to the price you pay at the register. The store collects it and sends it to the government.

$\text{Total Cost} = \text{Selling Price} + (\text{Selling Price} \times \text{Sales Tax Rate})$

Step-by-step example: An item costs $\$100$ and the sales tax rate is 8%.

1. Convert the percent to a decimal: $8\% = 0.08$
2. Multiply the price by the tax rate: $\$100 \times 0.08 = \$8$
3. Add the tax to the original price: $\$100 + \$8 = \$108$

The total cost is $\$108$.

A few things to know about sales tax:

• Rates vary by state and city. Some states (like Oregon and Montana) have no sales tax at all, while others go above 10%.
• Certain items are often exempt or taxed at a lower rate, like groceries and prescription medications.
• On a test, the tax rate will always be given to you. In real life, you'd look it up for your location.

Commission Amount Determination

A commission is a percentage of a sale that a salesperson earns as pay. It rewards them for selling more.

$\text{Commission} = \text{Selling Price} \times \text{Commission Rate}$

Step-by-step example: A salesperson sells an item for $\$500$ at a 10% commission rate.

1. Convert the percent to a decimal: $10\% = 0.10$
2. Multiply: $\$500 \times 0.10 = \$50$

The salesperson earns $\$50$ in commission.

Commission rates depend on the industry and the product. Real estate agents might earn 3–6% on a home sale, while a retail employee might earn a much smaller percentage. Some companies use tiered structures where the rate increases as the salesperson sells more.

Discount Application and Final Costs

A discount is a percentage that gets subtracted from the original price. Notice this is the opposite direction from sales tax.

$\text{Discounted Price} = \text{Original Price} - (\text{Original Price} \times \text{Discount Rate})$

Step-by-step example: A jacket originally costs $\$80$ and is 25% off.

1. Convert the percent to a decimal: $25\% = 0.25$
2. Find the discount amount: $\$80 \times 0.25 = \$20$
3. Subtract from the original price: $\$80 - \$20 = \$60$

The sale price is $\$60$.

Stacking multiple discounts: When two discounts apply to the same item, you don't just add the percentages together. You apply them one at a time, each to the already-reduced price.

Example: An item costs $\$100$ with a 20% discount and then an additional 10% discount.

1. Apply the first discount: $\$100 - (\$100 \times 0.20) = \$80$

2. Apply the second discount to the new price: $\$80 - (\$80 \times 0.10) = \$72$

The final price is $\$72$, not $\$70$. A common mistake is adding 20% + 10% = 30% and taking 30% off the original. That would give you $\$70$, which is wrong because the second discount applies to the already-reduced price, not the original.

Markup Pricing Strategies

Markup is the amount a store adds to what they paid for an item so they can make a profit. It works just like sales tax: find a percent, then add.

$\text{Selling Price} = \text{Cost} + (\text{Cost} \times \text{Markup Rate})$

Step-by-step example: A store buys a shirt for $\$50$ wholesale and marks it up 40%.

1. Convert the percent to a decimal: $40\% = 0.40$
2. Find the markup amount: $\$50 \times 0.40 = \$20$
3. Add to the cost: $\$50 + \$20 = \$70$

The store sells the shirt for $\$70$.

Markup rates need to be high enough to cover the store's expenses (rent, employee wages, shipping) and still leave room for profit. That's why the price you pay in a store is always higher than what the store paid for the item.

Profit and Revenue Analysis

These terms describe how businesses track their money:

• Revenue is the total income from sales before any costs are subtracted.
• Gross profit is revenue minus the cost of the goods sold. It doesn't account for other expenses yet.
• Net profit is what's left after all expenses (rent, wages, utilities, etc.) are subtracted from gross profit. This is the "real" profit.
• Profit margin is net profit expressed as a percentage of revenue. It tells you how many cents of each dollar in sales the business actually keeps.
• Break-even point is the sales volume where total revenue exactly equals total costs, meaning zero profit and zero loss. Anything above that point is profit.