Select the correct answer.

Blake has [tex]$b$[/tex] baseball cards. His aunt gave him more cards, increasing his total number of cards by [tex]$25\%$[/tex]. Which expression represents Blake's total number of cards now?

A. [tex]b + 0.25[/tex]
B. [tex]b - 0.75b[/tex]
C. [tex]1.25b[/tex]
D. [tex]0.75b[/tex]



Answer :

Sure! Let's solve this step-by-step.

1. Initial Number of Cards:
Let the initial number of baseball cards Blake has be [tex]\( b \)[/tex].

2. Percentage Increase:
Blake's aunt increases his total number of cards by [tex]\( 25\% \)[/tex]. To find how many cards this is, we calculate [tex]\( 25\% \)[/tex] of [tex]\( b \)[/tex].

[tex]\[ \text{Increase} = 0.25 \times b \][/tex]

3. Total Number of Cards After the Increase:
Now, we need to add this increase to the initial number of cards to find the new total.

[tex]\[ \text{New Total} = b + (0.25 \times b) \][/tex]

4. Simplifying the Expression:
We can factor out the [tex]\( b \)[/tex] in the expression above:

[tex]\[ \text{New Total} = b (1 + 0.25) \][/tex]
[tex]\[ \text{New Total} = 1.25 \times b \][/tex]

Therefore, the expression that represents Blake's total number of cards now is:

[tex]\[ \boxed{1.25b} \][/tex]

Thus, the correct answer is:
C. [tex]\( 1.25 b \)[/tex]