The sum of the ages of Arturo, Benny, and Carlos is 41 years. Twice Arturo's age exceeds the sum of Benny and Carlos's ages by one year. Five years ago, Benny was 2 years more than twice as old as Carlos. Find their ages now

Arturo is 14 years

Benny is 17 years

Carlos is 10 years

Step-by-step 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

step-by-step explanation:

descending order means to order the polynomials from the term with the largest exponent to the term with the smallest exponent.  

therefore, the correct answer is d.  

5=812a+9+3

step 1: simplify both sides of the equation.

5=812a+9+3

5=(812a)+(9+3)(combine like terms)

5=812a+12

5=812a+12

step 2: flip the equation.

812a+12=5

step 3: subtract 12 from both sides.

812a+12−12=5−12

812a=−7

step 4: divide both sides by 812.

812a /812 = -7/812

a= -1/116

so the answer is

a=   -1/116