Let Carl's age be \( x \). Then, Jazmin's age is \( x + 5 \) (since she is 5 years older than Carl). Lucas's age is \( 2x \) (since he is twice as old as Carl).
The sum of their ages can be expressed as:
\[ x + (x + 5) + 2x = 47 \]
Now, simplify the equation:
\[ x + x + 5 + 2x = 47 \] \[ 4x + 5 = 47 \]
Subtract 5 from both sides:
\[ 4x = 42 \]
Now, divide by 4:
\[ x = 10.5 \]
Now we can find the ages of each person:
- Carl's age: \( x = 10.5 \)
- Jazmin's age: \( x + 5 = 10.5 + 5 = 15.5 \)
- Lucas's age: \( 2x = 2 \times 10.5 = 21 \)
So, the ages are:
- Carl: 10.5 years
- Jazmin: 15.5 years
- Lucas: 21 years