Let X be the age of Cooper.

So Dante is X*2 years old and Maria is X*2 + 1 year old.

The sum of Cooper’s, Dante’s, and Maria’s ages is X + (X*2) + (X*2 + 1) = 31.

Combining like terms, we get X*5 + 1 = 31.

Subtracting one from both sides, we get X*5 = 30.

Dividing both sides by 5, we get X = 6 years old.

# Answer

6
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
The sum of Cooper’s, Dante’s, and Maria’s ages is 31. Dante is twice as old as Cooper. Maria is one year older than Dante. How old is Cooper?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
6
The sum of Cooper’s, Dante’s, and Maria’s ages is 31. Dante is twice as old as Cooper. Maria is one year older than Dante. How old is Cooper?
train