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.

Let's solve the problem step by step to find Ed and Ted's ages:

1. Understand the Problem:
- We know that Ed is 7 years older than Ted.
- We also know that Ed's age is [tex]$\frac{3}{2}$[/tex] times Ted's age.

2. Set Up the Equation:
- Let Ted's age be [tex]$ t $[/tex].
- Then Ed's age can be expressed as [tex]$ t + 7 $[/tex].
- According to the problem, Ed's age is also [tex]$\frac{3}{2}$[/tex] times Ted's age, which gives us the equation:
[tex]\[
t + 7 = \frac{3}{2} \times t
\][/tex]

3. Solve the Equation:
- To eliminate the fraction, multiply both sides of the equation by 2:
[tex]\[
2(t + 7) = 3t
\][/tex]
- Distribute and simplify:
[tex]\[
2t + 14 = 3t
\][/tex]
- Move all terms involving [tex]$ t $[/tex] to one side:
[tex]\[
14 = 3t - 2t
\][/tex]
- Simplify further:
[tex]\[
14 = t
\][/tex]

4. Find Each Age:
- Ted's age, [tex]$ t $[/tex], is 14.
- Ed's age, which is [tex]$ t + 7 $[/tex], is [tex]$ 14 + 7 = 21 $[/tex].

So, 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.