Applications of Percentages
A percentage is a number that represents the fractional part out of 100 (per cent literally means per one hundred). Thus 87% means \( \frac{87}{100}\) or \(0.87.\)
Because percentages are always out of 100, they are generally simpler to use than fractions when comparing quantities. Common uses of percentages include taxes, discounts, markups, profits, losses, and interest rates.
Tips, Taxes, and Discounts
When people tip others for their service, they generally use a percentage to calculate the amount to tip. For example, if you decide to tip 20% on a $50 meal, you would leave a \((0.20)($50) = $10\) tip.
Likewise, taxes and discounts are often percentage-based. For example, sales tax in a city might be 8% and a store might have a "40% OFF" sale.
We can calculate tips, taxes, and discounts by calculating percentages of quantities and then adding or subtracting as necessary.
Drew buys $70 worth of new clothing. If he must pay a 6% sales tax, what will his total be?
6% of $70 is \((0.06)($70) = $4.20.\)
Therefore, Drew's total bill will be \($70 + $4.20 = $74.20.\)
Anya gets a 30% sale discount and 10% club discount for the $200 jacket that she would like to purchase. How much does she have to pay for the jacket?
To begin, Anya gets a 30% discount, so she is paying 70% of the cost of the jacket, or \((0.7)($200) = $140.\)
Next, Anya gets a 10% discount, so she is paying 90% of the remaining cost of the jacket, or \((0.9)($140) = $126.\)
Magan is going to buy a new skirt. But the skirt that she wants to buy is offered at different prices and discount rates depending on the shops. The list prices and discount rates offered are shown in the table below. Choose the shop where she can buy it at the lowest price.
Percentage Change
Percentage change is the measure of change in a quantity expressed as a percent.
Percentage change is
\[ \frac {\text{amount of change}} {\text{ original value}} \times 100 \%.\]
The price of a sweatshirt changed from \( $20 \) to \( $30 \). Find the percentage change in the price of the sweatshirt.
The change in price of the sweatshirt is \($10,\) and the original price of the sweatshirt was \($20.\) Therefore, the percentage change in the price of the sweatshirt is
\[\frac{10}{20} × 100 \% = 50\%.\]
Imagine a city with 10,000 people at the beginning of a year. Given that the population at the end of that year is 9,500, compute the percentage change of the population.
The population changed by \(10000-9500 = 500\) people.The percent change in the population is \[\frac{500}{10000} \times 100 \% = 5\%.\]
The price of a lunch is \($10\). If its price increases by \(10\)%, then what is the new price?
10% of $10 is $1, so the new price is \($10 +$1 = $11.\)