Benett is twice as old as his daughter Alisa. Who is three years younger than her brother Neal. If the sum of their ages is 63, how old

Options

A. 15
B. 18
C. 50
D. 23

Answer

To find the ages of Benett, Alisa, and Neal based on the information provided, we can follow these steps:

### Step 1: Define Variables
Let Neal's age be represented by \( x \).

### Step 2: Express Alisa's Age
Since Alisa is three years younger than Neal, we can express Alisa's age as:
\[ \text{Alisa's age} = x - 3 \]

### Step 3: Express Benett's Age
Benett is twice as old as Alisa. Therefore, we can express Benett's age as:
\[ \text{Benett's age} = 2 \times \text{Alisa's age} = 2(x - 3) = 2x - 6 \]

### Step 4: Set Up the Equation
According to the problem, the sum of their ages is 63. We can write this as:
\[ \text{Benett's age} + \text{Alisa's age} + \text{Neal's age} = 63 \]
Substituting the expressions we have:
\[ (2x - 6) + (x - 3) + x = 63 \]

### Step 5: Simplify the Equation
Now, we simplify the left side:
\[ 2x - 6 + x - 3 + x = 63 \]
Combining like terms:
\[ 4x - 9 = 63 \]

### Step 6: Solve for \( x \)
Next, we isolate \( x \) by adding 9 to both sides:
\[ 4x = 63 + 9 \]
\[ 4x = 72 \]
Now, divide both sides by 4:
\[ x = \frac{72}{4} = 18 \]

### Step 7: Conclusion
Neal's age is \( 18 \) years.

### Step 8: Find the Ages of Alisa and Benett
- Alisa's age: \( x - 3 = 18 - 3 = 15 \) years.
- Benett's age: \( 2(x - 3) = 2(15) = 30 \) years.

### Summary of Ages
- Neal: 18 years
- Alisa: 15 years
- Benett: 30 years