Consumer Math with Percents

Consumer math involves using percentages in everyday real-world situations, like shopping or eating at a restaurant. The most common scenarios involve discounts (which lower the price) and taxes, tips, or markups (which increase the price).

Discounts (Markdowns)

A discount is an amount subtracted from the original price.

Example: An item costs \60$and is discounted by$20%$. What is the sale price?

1. Find the discount amount: $20\% = 0.20$ $0.20 \times 60 = 12$
2. Subtract from the original price: $60 - 12 = 48$

Shortcut: If an item is $20\%$ off, you are paying $80\%$ of the original price. $0.80 \times 60 = 48$ The sale price is \48$.

Sales Tax and Tips

Sales tax and tips are extra charges added to your total bill.

Example: A meal costs \45$. You leave a$15%$ tip. What is the total?

1. Find the tip amount: $15\% = 0.15$ $0.15 \times 45 = 6.75$
2. Add the tip to the original bill: $45 + 6.75 = 51.75$

Shortcut: To add $15\%$, you can multiply the original amount by $1.15$ ($100\% + 15\%$). $45 \times 1.15 = 51.75$ The total is \51.75$.

Markups and Profit

Stores buy items at a wholesale cost and add a markup (a percentage of the cost) to make a profit.

Example: A store buys a shirt for \30$and marks it up by$40%$. What is the selling price?

1. Find the markup amount: $40\% = 0.40$ $0.40 \times 30 = 12$
2. Add the markup to the cost: $30 + 12 = 42$ The selling price is \42$.

Combining Multiple Percent Calculations

When a problem has multiple steps—like a discount followed by sales tax—always calculate them one at a time. Never just add or subtract the percentages together, because the tax is applied to the new, discounted price, not the original price.

Example: A \60$item is discounted$20%$, then a$5%$ tax is added. What is the final price?

Step 1: Apply the discount. We already found that a $20\%$ discount on \60$makes the sale price$$48$.

Step 2: Apply the tax to the sale price. Now, calculate the $5\%$ tax on the \48$sale price (not the$$60$). $5\% = 0.05$ $0.05 \times 48 = 2.40$

Finally, add the tax to the sale price: $48 + 2.40 = 50.40$

The final price you pay at the register is \50.40$.