Answer :
Sure! Let's solve the problem step-by-step.
Let's use [tex]\( t \)[/tex] to represent Ted's age and [tex]\( e \)[/tex] to represent Ed's age.
We have two pieces of information:
1. Ed is 7 years older than Ted.
2. Ed's age is [tex]\(\frac{3}{2}\)[/tex] times Ted's age.
We can write these statements as equations:
1. [tex]\( e = t + 7 \)[/tex] (Ed is 7 years older than Ted)
2. [tex]\( e = \frac{3}{2} t \)[/tex] (Ed's age is [tex]\(\frac{3}{2}\)[/tex] times Ted's age)
We will solve these equations step-by-step:
### Step 1: Express one equation in terms of [tex]\( t \)[/tex]
From the second equation:
[tex]\[ e = \frac{3}{2} t \][/tex]
### Step 2: Substitute [tex]\( e \)[/tex] in the first equation
Substitute [tex]\( e \)[/tex] in the first equation with [tex]\(\frac{3}{2} t \)[/tex]:
[tex]\[ \frac{3}{2} t = t + 7 \][/tex]
### Step 3: Solve for [tex]\( t \)[/tex]
Subtract [tex]\( t \)[/tex] from both sides to get all terms involving [tex]\( t \)[/tex] on one side:
[tex]\[ \frac{3}{2} t - t = 7 \][/tex]
Combine like terms:
[tex]\[ \left(\frac{3}{2} - 1\right) t = 7 \][/tex]
[tex]\[ \frac{1}{2} t = 7 \][/tex]
Multiply both sides by 2 to solve for [tex]\( t \)[/tex]:
[tex]\[ t = 7 \times 2 \][/tex]
[tex]\[ t = 14 \][/tex]
So, Ted is 14 years old.
### Step 4: Find Ed's age
Use the first equation [tex]\( e = t + 7 \)[/tex] to find [tex]\( e \)[/tex]:
[tex]\[ e = 14 + 7 \][/tex]
[tex]\[ e = 21 \][/tex]
So, Ed is 21 years old.
Thus, the correct answer is:
B. Ted is 14 years old, and Ed is 21 years old.
Let's use [tex]\( t \)[/tex] to represent Ted's age and [tex]\( e \)[/tex] to represent Ed's age.
We have two pieces of information:
1. Ed is 7 years older than Ted.
2. Ed's age is [tex]\(\frac{3}{2}\)[/tex] times Ted's age.
We can write these statements as equations:
1. [tex]\( e = t + 7 \)[/tex] (Ed is 7 years older than Ted)
2. [tex]\( e = \frac{3}{2} t \)[/tex] (Ed's age is [tex]\(\frac{3}{2}\)[/tex] times Ted's age)
We will solve these equations step-by-step:
### Step 1: Express one equation in terms of [tex]\( t \)[/tex]
From the second equation:
[tex]\[ e = \frac{3}{2} t \][/tex]
### Step 2: Substitute [tex]\( e \)[/tex] in the first equation
Substitute [tex]\( e \)[/tex] in the first equation with [tex]\(\frac{3}{2} t \)[/tex]:
[tex]\[ \frac{3}{2} t = t + 7 \][/tex]
### Step 3: Solve for [tex]\( t \)[/tex]
Subtract [tex]\( t \)[/tex] from both sides to get all terms involving [tex]\( t \)[/tex] on one side:
[tex]\[ \frac{3}{2} t - t = 7 \][/tex]
Combine like terms:
[tex]\[ \left(\frac{3}{2} - 1\right) t = 7 \][/tex]
[tex]\[ \frac{1}{2} t = 7 \][/tex]
Multiply both sides by 2 to solve for [tex]\( t \)[/tex]:
[tex]\[ t = 7 \times 2 \][/tex]
[tex]\[ t = 14 \][/tex]
So, Ted is 14 years old.
### Step 4: Find Ed's age
Use the first equation [tex]\( e = t + 7 \)[/tex] to find [tex]\( e \)[/tex]:
[tex]\[ e = 14 + 7 \][/tex]
[tex]\[ e = 21 \][/tex]
So, Ed is 21 years old.
Thus, the correct answer is:
B. Ted is 14 years old, and Ed is 21 years old.
