To solve the problem of how to express Kyle's age [tex]\( k \)[/tex] in terms of Mara's age [tex]\( m \)[/tex] given that Mara is 3 years older than Kyle, let's go through the steps carefully:
1. Identify the relationship between Mara's age and Kyle's age:
- We are given that Mara is 3 years older than Kyle.
- In mathematical terms, this relationship can be written as: [tex]\( m = k + 3 \)[/tex], where [tex]\( m \)[/tex] is Mara's age and [tex]\( k \)[/tex] is Kyle's age.
2. Rearrange the equation to solve for Kyle's age [tex]\( k \)[/tex]:
- Starting with the equation [tex]\( m = k + 3 \)[/tex]:
- We want to isolate [tex]\( k \)[/tex] on one side of the equation. To do this, subtract 3 from both sides of the equation:
[tex]\[
m - 3 = k + 3 - 3
\][/tex]
- Simplifying this, we get:
[tex]\[
k = m - 3
\][/tex]
3. Confirm the rearranged equation:
- The correct expression for Kyle's age [tex]\( k \)[/tex] in terms of Mara's age [tex]\( m \)[/tex] is [tex]\( k = m - 3 \)[/tex].
4. Identify the correct answer choice:
- Reviewing the given answers:
- (A) [tex]\( k = m + 3 \)[/tex]
- (B) [tex]\( k = m - 3 \)[/tex]
- (C) [tex]\( k = 3m \)[/tex]
- (D) [tex]\( k = 3 - m \)[/tex]
The correct answer is [tex]\( \boxed{B} \)[/tex], which corresponds to [tex]\( k = m - 3 \)[/tex].
