Let's carefully analyze the given problem and solve it step-by-step.
We are told that Cole's age is 3 years less than his sister Tina's age. Let's break this information down:
1. Identify the Variables:
- Let [tex]\( t \)[/tex] be Tina's age.
- Cole's age is given as 18 years.
2. Translate the Statement into an Equation:
- We know that Cole's age is 3 years less than Tina's age.
- This relationship can be written as: [tex]\( t - 3 = 18 \)[/tex].
3. Solve the Equation for Tina's Age:
- We need to solve for [tex]\( t \)[/tex] in the equation [tex]\( t - 3 = 18 \)[/tex].
- To isolate [tex]\( t \)[/tex], add 3 to both sides of the equation:
[tex]\[
t - 3 + 3 = 18 + 3
\][/tex]
[tex]\[
t = 21
\][/tex]
Thus, Tina's age is 21.
Now, let's match this solution with the given options:
- Option A: The equation [tex]\( t - 3 = 18 \)[/tex] correctly represents the situation, and we found that Tina is 21 years old.
- Option B: The equation [tex]\( t + 3 = 18 \)[/tex] is incorrect, and it yields [tex]\( t = 15 \)[/tex], which does not align with our solution.
- Option C: The equation [tex]\( 3 - t = 18 \)[/tex] is incorrect and yields an invalid result.
- Option D: The equation [tex]\( -3 - t = 18 \)[/tex] is incorrect and also yields an invalid result.
Therefore, Option A is accurate:
- The correct equation is [tex]\( t - 3 = 18 \)[/tex].
- Tina's age is 21.
Hence, the correct answer is:
A. The equation that represents this situation is [tex]\( t - 3 = 18 \)[/tex]. Tina is 21.
