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Answer :
Sure! Let's solve the problem step-by-step to find out how old Ed and Ted are.
1. Understand the relationships:
- Ed is 7 years older than Ted.
- Ed's age is also [tex]\(\frac{3}{2}\)[/tex] times Ted's age.
2. Set up equations:
- Let's use [tex]\( t \)[/tex] to represent Ted's age.
- Since Ed is 7 years older than Ted, we can express Ed's age as [tex]\( t + 7 \)[/tex].
- According to the second relationship, Ed's age can also be expressed as [tex]\(\frac{3}{2} \times t\)[/tex].
3. Formulate the equation:
- We have two expressions for Ed's age: [tex]\( t + 7 \)[/tex] and [tex]\(\frac{3}{2} \times t\)[/tex].
- Set these two expressions equal to each other:
[tex]\[
t + 7 = \frac{3}{2} \times t
\][/tex]
4. Solve for Ted's age:
- Subtract [tex]\( t \)[/tex] from both sides of the equation to isolate [tex]\( t \)[/tex]:
[tex]\[
7 = \frac{3}{2} \times t - t
\][/tex]
- Simplify the right side:
[tex]\[
7 = \frac{1}{2} \times t
\][/tex]
- To solve for [tex]\( t \)[/tex], multiply both sides by 2:
[tex]\[
14 = t
\][/tex]
- So, Ted is 14 years old.
5. Find Ed's age:
- Since Ed is 7 years older than Ted, we add 7 to Ted's age:
[tex]\[
t + 7 = 14 + 7 = 21
\][/tex]
- Thus, Ed is 21 years old.
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. Understand the relationships:
- Ed is 7 years older than Ted.
- Ed's age is also [tex]\(\frac{3}{2}\)[/tex] times Ted's age.
2. Set up equations:
- Let's use [tex]\( t \)[/tex] to represent Ted's age.
- Since Ed is 7 years older than Ted, we can express Ed's age as [tex]\( t + 7 \)[/tex].
- According to the second relationship, Ed's age can also be expressed as [tex]\(\frac{3}{2} \times t\)[/tex].
3. Formulate the equation:
- We have two expressions for Ed's age: [tex]\( t + 7 \)[/tex] and [tex]\(\frac{3}{2} \times t\)[/tex].
- Set these two expressions equal to each other:
[tex]\[
t + 7 = \frac{3}{2} \times t
\][/tex]
4. Solve for Ted's age:
- Subtract [tex]\( t \)[/tex] from both sides of the equation to isolate [tex]\( t \)[/tex]:
[tex]\[
7 = \frac{3}{2} \times t - t
\][/tex]
- Simplify the right side:
[tex]\[
7 = \frac{1}{2} \times t
\][/tex]
- To solve for [tex]\( t \)[/tex], multiply both sides by 2:
[tex]\[
14 = t
\][/tex]
- So, Ted is 14 years old.
5. Find Ed's age:
- Since Ed is 7 years older than Ted, we add 7 to Ted's age:
[tex]\[
t + 7 = 14 + 7 = 21
\][/tex]
- Thus, Ed is 21 years old.
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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