Answer :
To solve the problem, we need to find the ages of Ed and Ted based on the given information:
1. Ed is 7 years older than Ted.
2. Ed's age is [tex]\( \frac{3}{2} \)[/tex] times Ted's age.
Let's use these facts to set up some equations.
- Let [tex]\( T \)[/tex] represent Ted's age.
- According to the first piece of information, Ed's age can be expressed as [tex]\( E = T + 7 \)[/tex].
- According to the second piece of information, Ed's age is also [tex]\( E = \frac{3}{2} \times T \)[/tex].
Now, we have two expressions for Ed's age:
1. [tex]\( E = T + 7 \)[/tex]
2. [tex]\( E = \frac{3}{2} \times T \)[/tex]
Since both expressions equal Ed's age, we can set them equal to each other:
[tex]\[ T + 7 = \frac{3}{2} \times T \][/tex]
To solve for Ted's age ([tex]\( T \)[/tex]), follow these steps:
- Start by clearing the fraction by multiplying every term in the equation by 2 to get rid of the fraction:
[tex]\[ 2(T + 7) = 3T \][/tex]
- Distribute the 2 on the left side:
[tex]\[ 2T + 14 = 3T \][/tex]
- Next, move all terms involving [tex]\( T \)[/tex] to one side of the equation by subtracting [tex]\( 2T \)[/tex] from both sides:
[tex]\[ 14 = 3T - 2T \][/tex]
- Simplify the equation:
[tex]\[ 14 = T \][/tex]
Ted is 14 years old.
Now, use Ted's age to find Ed's age by substituting back into one of the original expressions for Ed's age:
[tex]\[ E = T + 7 \][/tex]
[tex]\[ E = 14 + 7 \][/tex]
[tex]\[ E = 21 \][/tex]
Ed is 21 years old.
The correct answer is:
B. Ted is 14 years old, and Ed is 21 years old.
1. Ed is 7 years older than Ted.
2. Ed's age is [tex]\( \frac{3}{2} \)[/tex] times Ted's age.
Let's use these facts to set up some equations.
- Let [tex]\( T \)[/tex] represent Ted's age.
- According to the first piece of information, Ed's age can be expressed as [tex]\( E = T + 7 \)[/tex].
- According to the second piece of information, Ed's age is also [tex]\( E = \frac{3}{2} \times T \)[/tex].
Now, we have two expressions for Ed's age:
1. [tex]\( E = T + 7 \)[/tex]
2. [tex]\( E = \frac{3}{2} \times T \)[/tex]
Since both expressions equal Ed's age, we can set them equal to each other:
[tex]\[ T + 7 = \frac{3}{2} \times T \][/tex]
To solve for Ted's age ([tex]\( T \)[/tex]), follow these steps:
- Start by clearing the fraction by multiplying every term in the equation by 2 to get rid of the fraction:
[tex]\[ 2(T + 7) = 3T \][/tex]
- Distribute the 2 on the left side:
[tex]\[ 2T + 14 = 3T \][/tex]
- Next, move all terms involving [tex]\( T \)[/tex] to one side of the equation by subtracting [tex]\( 2T \)[/tex] from both sides:
[tex]\[ 14 = 3T - 2T \][/tex]
- Simplify the equation:
[tex]\[ 14 = T \][/tex]
Ted is 14 years old.
Now, use Ted's age to find Ed's age by substituting back into one of the original expressions for Ed's age:
[tex]\[ E = T + 7 \][/tex]
[tex]\[ E = 14 + 7 \][/tex]
[tex]\[ E = 21 \][/tex]
Ed is 21 years old.
The correct answer is:
B. Ted is 14 years old, and Ed is 21 years old.
