Steven has 55 baseball cards. Steven and Lucas have more than 71 baseball cards together. Which of the following inequalities represents the number of baseball cards the two boys have?

A. [tex]55 - b \ \textgreater \ 71[/tex]
B. [tex]55 + b \ \textless \ 71[/tex]
C. [tex]b \ \textgreater \ 55 + 71[/tex]
D. [tex]55 + b \ \textgreater \ 71[/tex]

Sure, let's break down the problem step-by-step.

Problem Statement:
Steven has 55 baseball cards. Combined, Steven and Lucas have more than 71 baseball cards. We need to determine the correct inequality that represents the number of baseball cards the two boys have together.

Step-by-Step Solution:

1. Identify the number of cards Steven has:
Steven has 55 baseball cards.

2. Define the variable for Lucas's cards:
Let [tex]\( b \)[/tex] be the number of baseball cards Lucas has.

3. Formulate the inequality:
According to the problem, together they have more than 71 baseball cards. So, the number of Steven's cards plus Lucas's cards must be greater than 71.
[tex]\[
55 + b > 71
\][/tex]

4. Matching with the given options:
We now compare the inequality we formulated with the given multiple-choice options:
- A. [tex]\( 55 - b > 71 \)[/tex]
- B. [tex]\( 55 + b < 71 \)[/tex]
- C. [tex]\( b > 55 + 71 \)[/tex]
- D. [tex]\( 55 + b > 71 \)[/tex]

The correct inequality that matches our formulation, [tex]\( 55 + b > 71 \)[/tex], is option D.

Conclusion:
The inequality that represents the number of baseball cards Steven and Lucas have together is:
[tex]\[
\boxed{D. \ 55 + b > 71}
\][/tex]