Question

Benjamin's age is 6 years less than twice Lucas's age. If Benjamin is 12 years old, how old is Lucas? Choose the answer below that is a viable solution to this problem.

Answer 1

9

Explanation:

Let's use the information given to find Lucas's age.

Benjamin's age is 12 years old, and it is 6 years less than twice Lucas's age. So we can write this as an equation:

Benjamin's age = 2 * Lucas's age - 6

Substitute Benjamin's age with 12:

12 = 2 * Lucas's age - 6

Now, add 6 to both sides of the equation:

12 + 6 = 2 * Lucas's age

18 = 2 * Lucas's age

Now, divide both sides by 2:

18 / 2 = Lucas's age

Lucas's age = 9

So, Lucas is 9 years old. Therefore, the viable solution to this problem is 9

Answer 2

Answer: The required age of Luca is 9 years.

Step-by-step explanation: Given that Benjamin's age is 6 years less than twice Lucas's age and Benjamin is 12 years old.

We are to find Luca's age.

Let x and y represents Luca's age and Benjamin's age respectively.

Then, according to the given information, we have

`y=2x-6~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\y=12~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)`

Substituting the value of y from equation (ii) in (i), we get

`y=2x-6\\\\\Rightarrow 12=2x-6\\\\\Rightarrow 2x=12+6\\\\\Rightarrow 2x=18\\\\\Rightarrow x=(18)/(2)\\\\\Rightarrow x=9.`

Thus, the required age of Luca is 9 years.