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Answer :
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.
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.
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