Answer: Arturo is 14 years
Benny is 17 years
Carlos is 10 years
Explanation:
Let x represent the age of Arturo.
Let y represent the age of Benny.
Let z represent the age of Carlos.
The sum of the ages of Arturo, Benny, and Carlos is 41 years. It means that
x + y + z = 41- - - - - - - - - - - - -1
Twice Arturo's age exceeds the sum of Benny and Carlos's ages by one year. It means that
2x = y + z + 1- - - - - - - - - 2
Five years ago, Benny was 2 years more than twice as old as Carlos. It means that
y - 5 = 2(z - 5) + 2
y - 5 = 2z - 10 + 2
y = 2z - 8 + 5
y = 2z - 3
Substituting y = 2z - 3 into equation 2, it becomes
2x = 2z - 3 + z + 1
2x = 2z + z - 3 + 1
2x = 3z - 2
x = 3z/2 - 1
Substituting y = 2z - 3 and
x = 3z/2 - 1 into equation 1, it becomes
3z/2 - 1 + 2z - 3 + z = 41
Multiplying through by 2, it becomes
3z - 2 + 4z - 6 + 2z = 82
3z + 4z + 2z - 2 - 6 = 82
9z - 8 = 82
9z = 82 + 8 = 90
z = 90/9
z = 10
x = 3z/2 - 1 = (3 × 10)/2 - 1
x = 14
y = 2z - 3 = 2 × 10 - 3
y = 17