About Percent Equation
What is Percentage?
In mathematics, a percentage is an amount expressed as a part of 100. We denote a percentage value using the ‘%’ symbol.
For example, when we go shopping, we often see displays or boards with percentage discounts written on them. It could be “15% off” or “30% discount on all items”. Here, the discount is expressed as a percentage. Another example where we use percentage is to calculate the tax on bills or receipts.
What is the Percent Equation?
The percent equation enables you to find a part or ratio of an amount (or whole). Percent is denoted by a numerical value which is a part of 100 followed by the ‘%’ symbol. The percent denoting a part of a whole can be calculated using the following equation.
percent = \(\frac{\text{part}}{\text{whole}}\times100\)
With the help of this equation, we can represent “a is p percent of w” as:
a = p% \(\cdot \) w, known as the percent equation.
So there are three parts in the percent equation:
- the part,
- the percent, and
- the whole.
[Note: When using the percent equation, always express the percent as a fraction or a decimal.]
Solved Examples
Example 1 : 10 is what percent of 50?
Answer: As per the percent equation,
a = p% \(\cdot\) w.
10 = \(\frac{p}{100}~\cdot\) 50 Write p% as \(\frac{p}{100}\) and substitute 10 for a and 50 for w.
\(\frac{10}{50}=\frac{p}{100}\cdot\frac{50}{50}\) Divide both sides by 50.
\( \frac{1}{5}=\frac{p}{100}\) Simplify
\(20=p\) Multiply both sides by 100.
Therefore, 10 is 20% of 50.
Example 2: 45 is 60% of what number?
Answer: Let us use the percent equation to find the value.
As we know, a = p% \(\cdot\) w
Here, a = 45 and p% = 60%.
Substituting the values in the percent equation,
45 = 0.6 x w 60% is equal to 0.6 in decimal form.
75 = w Divide both sides by 0.6.
Thus, 45 is 60% of 75.
Example 3: Rachel bought groceries from a store. The total bill is $320 upon which a service tax of 15% is levied. How much tax did Rachel pay? Also, find the total amount paid by Rachel.
Answer:
Total bill amount = $320
Percent tax on total bill amount = 15%
As per the percent equation, a = p% \(\cdot\) w,
a = \(\frac{p}{100}~\cdot\) w Write p% as \( \frac{p}{100}\)
a = \(\frac{15}{100}\) x 320 Substitute 320 for w and 15 for p
= 48 Simplify
Total amount paid = Total bill amount + Tax
= 320 + 48
= 368
Hence the tax amount paid by Rachel is $48, and the total amount paid is $368.
The percent equation is used for determining ‘how much’ or ‘how many’ of a particular value (or whole).
Percentage can be defined as the numerical value which is a part of 100.
Percentage increase and decrease is a measure of how much a percentage value has changed.