Calculate discounts, markups, taxes, and tips

Discounts, markups, sales taxes, and tips are understood as percentage changes applied to an appropriate monetary base, such as the original price or subtotal; the percentage amount and final cost can be represented with equations or decimal multipliers such as $1-r$ and $1+r$ . Reasoning includes distinguishing the original amount from the adjusted amount, applying sequential changes in the stated order, and rounding money appropriately, while complex tax rules, compound financial models, and advanced inverse-percentage problems are outside this scope.

Detailed Explanation: Calculate discounts, markups, taxes, and tips

A percentage change is found by multiplying the correct starting amount by a decimal.

Discount: multiply by $1-r$
Markup, tax, or tip: multiply by $1+r$

Here, $r$ is the percentage written as a decimal. For example, $25\% = 0.25$ .

Example

A jacket costs 80 $. It is on sale for$ 25% $off, and then an$ 8%$ sales tax is added. What is the final cost?

Step 1: Find the sale price.

A $25\%$ discount means you pay $100\%-25\%=75\%$ of the original price.

80(1-0.25)=80(0.75)=60

The sale price is 60$.

Step 2: Add the tax to the sale price.

The tax is based on the sale price, not the original price. An $8\%$ tax means multiplying by $1.08$ .

60(1+0.08)=60(1.08)=64.80

Step 3: State the answer with money rounding.

The final cost is:

\boxed{\$64.80}

Always apply percentage changes to the amount that the problem identifies as the base. For changes in sequence, complete the first change before applying the next one.

Learn by doing: Calculate discounts, markups, taxes, and tips

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