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Two years ago, I was three times as old as my brother was. In three years’ time, I will be twice as old as my brother. How old are we now?

1 Answer

6 votes

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.

User Mdec
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