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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.

Answer :

To solve the problem of finding Ed and Ted's ages, we need to set up some equations based on the information given:

1. Relationship based on age difference:
- Ed is 7 years older than Ted. If we let Ted's age be [tex]\( x \)[/tex], then Ed's age would be [tex]\( x + 7 \)[/tex].

2. Relationship based on the fractional multiplication:
- Ed's age is also [tex]\(\frac{3}{2}\)[/tex] times Ted's age. So, we can write this as an equation:
[tex]\[
\text{Ed's age} = \frac{3}{2} \times \text{Ted's age}
\][/tex]
- Substitute Ed's age with [tex]\( x + 7 \)[/tex]:
[tex]\[
x + 7 = \frac{3}{2} \times x
\][/tex]

3. Solving the equation:
- Start with the equation:
[tex]\[
x + 7 = \frac{3}{2} \times x
\][/tex]
- To eliminate the fraction, you can multiply through by 2 (though we'll simplify without needing that for a basic solution view):
- Rearrange terms:
[tex]\[
x + 7 = \frac{3}{2}x
\][/tex]
- Subtract [tex]\( x \)[/tex] from both sides to get:
[tex]\[
7 = \frac{3}{2}x - x
\][/tex]
- Simplify the right side:
[tex]\[
7 = \frac{1}{2}x
\][/tex]

4. Isolate [tex]\( x \)[/tex]:
- Multiply both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = 14
\][/tex]
- So, Ted is 14 years old.

5. Find Ed's age:
- Since Ed is 7 years older than Ted:
[tex]\[
\text{Ed's age} = 14 + 7 = 21
\][/tex]

Hence, Ted is 14 years old, and Ed is 21 years old. Therefore, the correct answer is:

B. Ted is 14 years old, and Ed is 21 years old.

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