Percent Off — Calculation & Practice

Percent Discount

Say you're at the store and you see a cute bracelet that costs $\$12.$ You think to yourself, "This sucks. I only have $\$10$ on me, but I really want to buy this bracelet today." Suddenly, your eyes widen with glee. There's a tag on the bracelet indicating that it's $25\%$ off! What is the sale price of the bracelet? Can you afford it?

We can determine final prices of discounted items in two steps:

1. Calculate the discount percent of the original price.
2. Subtract the discount result from the original price.

Remember: $$\text{Final Price} = \text{Original Price} - \text{Discount Amount}$$

Let's see these steps in action using our bracelet example.

Since the bracelet is $\$9,$ you can afford it!

Important Note: Remember to subtract the discount amount from your original price! You are not done after Step One!

Let's do one more example

Step One: Calculate the discount percent of the original price

The original price of the book is $\$26.50,$ and there is a $40\%$ off discount. $$\begin{align} 40\% \text{ of } 26.50 &= \dfrac{40}{100} \times \dfrac{26.50}{1}\\ &=\dfrac{40 \times 26.50}{100}\\ &=\dfrac{1060}{100}\\ &=10.6 \end{align}$$ So, the discount amount is $\$10.60.$ Step Two: Subtract the discount amount from the original price

$$\text{Final Price} = \text{Original Price} - \text{Discount Amount}$$

Our original price is $\$26.50$ and our discount amount (which we just calculated) is $\$10.60.$ Thus, $$\begin{align} \text{Final Price}&= 26.50-10.60\\ &=15.90 \end{align}$$ So, the final sale price of the fractal book is $\$15.90.$ What a bargain!

So you've decided to buy an official Expii cowboy hat.

The hat originally cost $\$50$, but as a longtime user of the site, you get a $25\%$ discount. In other words, there is a $25$ percentage discount on the hat.

How much money do you save? How much does the hat cost you after the discount is applied?

How much money do you save?

Our overall goal is to find amount of the discount and sale price.

This question wants us to find $25\%$ of the original price, $\$50$. We can do this by multiplying the decimal equivalent of $25\%$ by $50$. Convert the decimal to a percentage. We do this by moving the decimal point to the right by two places.

$$25 \% = 0.25$$

Then we multiply this decimal by the original price.

$$0.25\cdot 50=12.5$$

This means that you save $\$12.50$ on the hat.

How much does the hat cost?

A $25\%$ discount means that the new price is $25\%$ of the original price subtracted from the original price. This means that we need to subtract the money you saved from the original price. $$50-12.5=37.5$$ This means that the new price of the hat is $\$37.50$.

Percent discount formula

In general, we can create a formula to solve for each of the variables (original price, discount price, and discount).

We can split up the calculation of the discount price into steps: multiplying the original price by the discount and subtracting this value from the original price. Mathematically, this can be represented as: $$\text{discount price}=\text{original price}-\text{original price}\cdot \text{discount}$$ We can then factor out the $\text{original price}$ from the right hand side to get our formula: $$\boxed{\text{discount price}=\text{original price}\cdot (1-\text{discount})}$$

(Video) Percent Discount

by Mario's Math Tutoring

This video by Mario's Math Tutoring goes over a bunch of great examples of how to calculate percent discount and prices related to percent discount.

$\large{\text{Summary}}$

Take an item which originally was $\$70$. Then, you see a tag that says it's $30\%$ off so we want to figure out how much it costs now.

Approach 1

The first way he approaches it is by first calculating what $30\%$ of $\$70$ is and then subtracting that from $\$70$.

We can calculate $30\%$ of $\$70$ by computing $\$70 \times 0.30$, since $30\%$ is $0.30$ in decimal form. Calculating this gives: $$\$70 \times 0.30 = \$21$$

Now, we got $30\%$ of $\$70$, but we want to find the price of the item after $30\%$ off. So, the end price is: $$\$70 - \$21 = \$49$$

Approach 2

The second way he approaches this is noticing that something which is $30\%$ off is $70\%$ of the real price. This is because the original price is $100\%$ of the original price, and if you take away $30\%$ from that, you're left with $70\%$. $$100\%-30\%=70\%$$

Now, we know the discounted price is $70\%$ of the original. So, we just need to find $70\%$ of $\$70$. $$\$70 \times 0.70 = \$49$$ Notice we get the same price as our other method!

Either way of thinking about percent discount is perfect, so feel free to try either and use that in practice.