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------------------------------------------------ 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:

1. We are given that Ed is 7 years older than Ted. So, if we let Ted's age be [tex]\( t \)[/tex], then Ed's age will be [tex]\( t + 7 \)[/tex].

2. We are also told that Ed's age is [tex]\(\frac{3}{2}\)[/tex] times Ted's age. This can be set up as the equation:
[tex]\[
t + 7 = \frac{3}{2} \times t
\][/tex]

3. To solve this equation, we can get rid of the fraction by multiplying every term by 2:
[tex]\[
2(t + 7) = 3t
\][/tex]

4. Expanding the left side gives:
[tex]\[
2t + 14 = 3t
\][/tex]

5. To isolate [tex]\( t \)[/tex], subtract [tex]\( 2t \)[/tex] from both sides:
[tex]\[
14 = 3t - 2t
\][/tex]

6. Simplifying gives:
[tex]\[
14 = t
\][/tex]

7. So, Ted is 14 years old.

8. To find Ed's age, remember Ed is 7 years older than Ted:
[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.