Ctrl+k

Calculate discounts, markups, taxes, and tips

Discounts, markups, sales taxes, and tips are understood as percent-of-a-quantity relationships: a discount subtracts a percentage of the original price, while a markup, tax, or tip adds a percentage of the appropriate base amount. Students represent these changes with percent equations and decimal multipliers, such as P(1−r)P(1-r) for a discount and P(1+r)P(1+r) for an increase, and distinguish the original price, percentage amount, and final total; compound interest, repeated percentage changes, and more advanced algebraic generalizations are not included.

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

A percentage change has three parts:

  • Original amount: the starting price or bill
  • Percentage amount: the discount, markup, tax, or tip
  • Final total: the amount after adding or subtracting

Convert the percent to a decimal before calculating:

  • Discount: multiply by 1−r1-r
  • Markup, tax, or tip: multiply by 1+r1+r

Here, rr is the decimal form of the percentage.

Example: A backpack costs 40.Thesalestaxis. The sales tax is 7%$. What is the total cost?

  1. Convert 7%7\% to a decimal:

7%=0.077\% = 0.07

  1. Find the tax amount by multiplying the original price by the tax rate:

40(0.07)=2.8040(0.07)=2.80

The sales tax is 2.80$.

  1. Add the tax to the original price:

40+2.80=42.8040+2.80=42.80

So, the total cost is:

$42.80\boxed{\$42.80}

You can also find the total in one step by using the increase multiplier:

40(1+0.07)=40(1.07)=42.8040(1+0.07)=40(1.07)=42.80

For a discount, subtract the percentage amount instead. For example, a 20%20\% discount uses the multiplier 1−0.20=0.801-0.20=0.80. Markups and tips use addition, just like sales tax.

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

Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill

    Practice with unlimited practice problems

    Percent growth of money (10% multiples)

      ?