Let's go through the problem step-by-step to determine the correct equation and Tina's age.
1. Understanding the Problem:
- Cole's age is 18 years.
- Cole's age is 3 years less than his sister Tina's age, denoted as [tex]\( t \)[/tex].
2. Setting Up the Equation:
- Since Cole's age is 3 years less than Tina's age, we can write this relationship as:
[tex]\[
\text{Cole's age} = t - 3
\][/tex]
- We know that Cole's age is 18, so we substitute 18 for Cole's age in the above equation:
[tex]\[
18 = t - 3
\][/tex]
- This equation represents the given situation.
3. Solving the Equation:
- To find Tina's age, we need to solve the equation [tex]\( 18 = t - 3 \)[/tex] for [tex]\( t \)[/tex].
- Add 3 to both sides to isolate [tex]\( t \)[/tex]:
[tex]\[
18 + 3 = t
\][/tex]
- Simplify the left side:
[tex]\[
21 = t
\][/tex]
- Therefore, Tina is 21 years old.
4. Verifying the Answer Choices:
- The equation that correctly represents the situation is [tex]\( t - 3 = 18 \)[/tex].
- According to our calculations, Tina's age is 21.
The correct answer is:
A. The equation that represents this situation is [tex]\( t-3=18 \)[/tex]. Tina is 21.
