To determine the ages of Ed and Ted, we will follow a step-by-step approach using the information given:
1. Let Ted's age be represented by [tex]\( t \)[/tex].
2. From the problem, we know Ed is 7 years older than Ted. Therefore, Ed's age can be written as [tex]\( t + 7 \)[/tex].
3. We also know that Ed's age is [tex]\(\frac{3}{2}\)[/tex] times Ted's age. Therefore, we can write the equation:
[tex]\[
t + 7 = \frac{3}{2} t
\][/tex]
4. To solve for [tex]\( t \)[/tex], we need to isolate [tex]\( t \)[/tex]. So let's start by clearing the fraction by multiplying both sides of the equation by 2:
[tex]\[
2(t + 7) = 3t
\][/tex]
5. This simplifies to:
[tex]\[
2t + 14 = 3t
\][/tex]
6. Next, we will get all the terms involving [tex]\( t \)[/tex] on one side of the equation. Subtract [tex]\( 2t \)[/tex] from both sides:
[tex]\[
14 = t
\][/tex]
7. Thus, Ted's age [tex]\( t \)[/tex] is 14 years.
8. To find Ed's age, we use the fact that Ed is 7 years older than Ted:
[tex]\[
\text{Ed's age} = t + 7 = 14 + 7 = 21 \text{ years}
\][/tex]
Therefore, Ted is 14 years old, and Ed is 21 years old. So the correct answer is:
B. Ted is 14 years old, and Ed is 21 years old.
