Let's go through the problem step by step.
1. Identify the Variables:
- Steven has 55 baseball cards.
- Let [tex]\( b \)[/tex] represent the number of baseball cards Lucas has.
2. Total Number of Cards:
- Together, Steven and Lucas have a sum of their baseball cards.
3. Define the Inequality:
- The problem states that the total number of baseball cards Steven and Lucas have together is more than 71. We can represent this with the inequality:
[tex]\[
55 + b > 71
\][/tex]
4. Analyze the Options:
- Option A: [tex]\( b > 55 + 71 \)[/tex] simplifies to [tex]\( b > 126 \)[/tex]
- This option is incorrect because it implies Lucas alone must have more than 126 cards.
- Option B: [tex]\( 55 - b > 71 \)[/tex]
- This option is incorrect as it implies if you subtract Lucas's cards from Steven's cards, it should be more than 71, which doesn't fit the context.
- Option C: [tex]\( 55 + b < 71 \)[/tex]
- This option is incorrect as it states their total is less than 71, which contradicts the given condition of having more than 71 cards together.
- Option D: [tex]\( 55 + b > 71 \)[/tex]
- This option correctly represents the condition given in the problem, where the combined total of Steven and Lucas's baseball cards is more than 71.
5. Conclusion:
- The correct inequality that represents the number of baseball cards the two boys have together is:
[tex]\[
55 + b > 71
\][/tex]
Therefore, the correct answer is:
D. [tex]\( 55+b>71 \)[/tex]
