- Blake starts with \(b\) cards.
- The increase is \(25\%\) of the total, which is \(0.25b\).
- The total cards after the increase is the sum of the original amount and the increase: \(b + 0.25b\).
- Simplifying this gives \(1.25b\), which is the correct expression.
- The final answer is \(\boxed{1.25b}\).
Explanation
- Analyzing the Increase in Baseball Cards
Blake starts with \(b\) baseball cards. When he receives more cards, his total increases by \(25\%\). To find the new total number of cards, we must calculate the original amount plus the amount he received from his aunt. The increase is equal to \(25\%\) of the original number of cards \(b\), which can be written as \(0.25b\). Therefore, the total number of cards after the increase is given by the expression \(b + 0.25b\).
- Simplifying the Expression and Identifying the Correct Option
To simplify the expression \(b + 0.25b\), we treat \(b\) as \(1b\). Combining the like terms, we get:
\[1b + 0.25b = (1 + 0.25)b = 1.25b\]
This algebraic expression represents the final total number of baseball cards. Comparing this with the provided options, we see that \(1.25b\) is the correct choice.
Examples
Understanding how to calculate percentage increases is a fundamental skill in everyday life. For instance, if you are shopping during a sale and want to calculate a total price after adding sales tax, you use the same principle: multiply the original price by (1 + tax rate). Similarly, if you invest money and receive interest, your new balance is calculated by increasing your initial principal by the given interest rate, which is a practical application of the algebraic expression \(b(1+p)\) for a percentage increase.