Question

The price of a notebook was \[\$3.50\] yesterday. Today, the price rose to \[\$3.75\]. How do you find the percentage increase?

Answer 1

Hint: This question is from the topic of algebra. In this question, we will find the percentage increase in the price of a notebook from yesterday. In solving this question, we will first find out the price difference from yesterday. After that, we will use the formula of percentage increase in price. After applying that formula, we will solve the further question. After that, we will get our answer.

Complete step by step solution:
Let us solve this question.
In this question, we have to find the percentage increase in price. We have given that the price of notebook was \[\$3.50\] yesterday. Now, the price of that notebook is \[\$3.75\] today.
So, let us first know the formula for increase in percentage.
The formula for percentage increase is in the following:
\[\%\text{ Increase in data}=\dfrac{\text{final data}-\text{initial data}}{\text{Initial data}}\times 100\]
So, let us first find out the Increment or increase in price of notebook.
 Increase in price = Final data (or final price) – initial data (or initial price) = \[\$3.75-\$3.50=\$0.25\]
And, we know that the initial data or price was \[\$3.50\].
So, using the formula of percent increase, we can write
\[\%\text{ Increase in price}=\dfrac{\text{Increase in price}}{\text{Initial price}}\times 100\]
Now, putting the values in the above equation, we can write the above equation as
\[\Rightarrow \%\text{ Increase in price}=\dfrac{\$0.25}{\$3.50}\times100\]
The above equation can also be written as
\[\Rightarrow \%\text{ Increase in price}=\dfrac{0.25}{3.50}\times 100\]
After multiplying and dividing the right side of the equation by 100, we can write the above equation as
\[\Rightarrow \%\text{ Increase in price}=\dfrac{0.25}{3.50}\times 100\times \dfrac{100}{100}=\dfrac{25}{350}\times 100\]
The above can also be written as
\[\Rightarrow \%\text{ Increase in price}=\dfrac{25}{35}\times 10=\dfrac{5}{7}\times 10=\dfrac{50}{7}\]
\[\Rightarrow \%\text{ Increase in price}=7.14\]
Hence, we got that the percentage increase in price from yesterday is 7.14%

Note: We should have a better knowledge in the topic of algebra to solve this type of question easily. We should know the formula of percentage increase. The formula for percentage increase is in the following:
\[\%\text{ Increase in data}=\dfrac{\text{final data}-\text{initial data}}{\text{Initial data}}\times 100\]
And, the formula for percentage decrease is in the following:
\[\%\text{ Decrease in data}=\dfrac{\text{initial data}-\text{final data}}{\text{Initial data}}\times 100\]