Answer:
You are 17 years old.
Your brother is 7 years old.
Explanation:
- We will need a system of equations to find your current age (x) and your brother's current age (y).
First equation:
We know that two years ago, you were three times as old as your brother:
Current age - two years= 3(Brother's current age - two years)
Thus, our first equation is given by:
x - 2= 3(y - 2)
To make it easier when solving, let's distribute the 3:
x - 2 = 3y - 6
Second equation:
We also know that in three years, you'll be twice as old as your bother:
Current age + 3 = 2(Brother's current age + three years)
Thus, our second equation is given by:
x + 3 = 2(y + 3)
Like we did for the first equation, let's distribute the 2:
x + 3 = 2y + 6
Method to solve: Substitution:
First, we can isolate x in the first equation:
(x - 2 = 3y - 6) + 2
x = 3y - 4
Solving for y (i.e., your brother's current age):
Now we can solve for y (i.e., your brother's current age) by substituting 3y - 4 for x in the second equation:
3y - 4 + 3 = 2y + 6
(3y - 1 = 2y + 6) + 1
(3y = 2y + 7) - 2y
y = 7
Thus, your brother is currently 7 years old.
Solving for x (i.e., your current age):
Now we can solve for x (i.e., your current age) by plugging in 7 for y in the first equation (i.e., x - 2 = 3y - 6):
x - 2 = 3(7) - 6
x - 2 = 21 - 6
(x - 2 = 15) + 2
x = 7
Thus, you are currently 17 years old.