Question

Together, Ben and Kyle have 43 fishing lures. Kyle, (K), has 15 more lures than Ben, (B). Which statements are correct for this situation?
Responses

A B + 42 = KB + 42 = K

B K + 15 = BK + 15 = B

C B + 15 = KB + 15 = K

D 43 − B = K43 − B = K

E 43 − 15 = B

Answer 1

Let's break down the situation step by step to understand the relationships between Ben's (B) and Kyle's (K) fishing lures.

1. We know:
- Together, they have 43 lures: \( B + K = 43 \)
- Kyle has 15 more lures than Ben: \( K = B + 15 \)

Now, we can use these equations to evaluate each statement:

**A**: \( B + 42 = K \)
- Substitute \( K \) with \( B + 15 \):
\( B + 42 = B + 15 \) is false because \( 42 \neq 15 \).

**B**: \( K + 15 = B \)
- This implies \( K = B - 15 \), which contradicts \( K = B + 15 \). So, this is false.

**C**: \( B + 15 = K \)
- This is true as it correctly reflects the relationship that Kyle has 15 more lures than Ben.

**D**: \( 43 - B = K \)
- We have \( K = B + 15 \). If we solve for \( K \) using the total:
\( K = 43 - B \). So we need to check consistency:
Set \( 43 - B = B + 15 \).
Rearranging gives: \( 43 - 15 = 2B \rightarrow 28 = 2B \rightarrow B = 14 \).
Then \( K = B + 15 = 14 + 15 = 29 \).
These values satisfy \( B + K = 43 \). So, it's true.

**E**: \( 43 - 15 = B \)
- This means \( B = 28 \) which contradicts the earlier found value of \( B = 14 \). So, this is false.

Summarizing:
- **Correct Statements**: C and D.
- **Incorrect Statements**: A, B, E.