Answer: Braulio is 15 years old, and Alejandro is 6 years old.
Step-by-step explanation:
Let's define:
B = Age of Braulio
A = Age of Alejandro.
"Three years from now, Braulio will be 3 times Alejandro's present age"
We can write this as:
B + 3 = 3*A
"At that time, Alejandro will then be half as old as Braulio"
A + 3 = (B + 3)/2
Then we have a system of equations:
B + 3 = 3*A
A + 3 = (B + 3)/2
To solve this, we first need to isolate one of the variables in one of the equations.
Let's isolate A in the second equation:
A = (B + 3)/2 - 3
Now we can replace this in the other equation to get:
B + 3 = 3*A
B + 3 = 3*((B + 3)/2 - 3)
B + 3 = (3/2)*B + 9/2 - 9
Now let´s move all the terms with B to the left side, and the other terms to the right side.
B - (3/2)*B = 9/2 - 9 - 3
-(1/2)*B = 9/2 - 18/2 - 6/2 = -15/2
B = (-2)*(-15/2) = 15
Braulio is 15 years old.
And from the first equation:
B + 3 = 3*A
15 + 3 = 3*A
18 = 3*A
18/3 = A = 6
Alejandro is 6 years old.
