Select the correct answer.

Ed is 7 years older than Ted. Ed's age is also [tex]$\frac{3}{2}$[/tex] times Ted's age. How old are Ed and Ted?

A. Ted is 15 years old, and Ed is 22 years old.
B. Ted is 14 years old, and Ed is 21 years old.
C. Ted is 13 years old, and Ed is 20 years old.
D. Ted is 12 years old, and Ed is 19 years old.

To determine the ages of Ed and Ted based on the given conditions, let's go through it step-by-step:

1. Understanding the Relationships:
- We know that Ed is 7 years older than Ted. This means if Ted's age is [tex]$ t $[/tex], Ed's age can be written as [tex]$ t + 7 $[/tex].
- We also know that Ed's age is [tex]$\frac{3}{2}$[/tex] times Ted's age. So, Ed's age can also be expressed as [tex]$\frac{3}{2} \times t$[/tex].

2. Setting Up the Equation:
- Since both expressions represent Ed's age, we can set them equal to each other:
[tex]\[
t + 7 = \frac{3}{2} \times t
\][/tex]

3. Solving the Equation:
- To eliminate the fraction, multiply every term by 2:
[tex]\[
2(t + 7) = 3t
\][/tex]
- Simplifying by distributing on the left side:
[tex]\[
2t + 14 = 3t
\][/tex]
- Rearrange the equation to isolate [tex]$ t $[/tex]:
[tex]\[
14 = 3t - 2t
\][/tex]
[tex]\[
14 = t
\][/tex]

4. Find Ed's Age:
- Now, we know Ted is 14 years old. Using the relationship [tex]$ t + 7 $[/tex] to find Ed's age:
[tex]\[
\text{Ed's age} = 14 + 7 = 21
\][/tex]

Therefore, Ted is 14 years old, and Ed is 21 years old. The correct answer is B. Ted is 14 years old, and Ed is 21 years old.