Question

One brother says of his younger brother: “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 they each now?

Answer 1

By setting up simultaneous equations based on the age relationships given, we find that the current age of the younger brother is 7 years old, and the older brother is 17 years old.

Step-by-step explanation:

Let's solve the problem involving the ages of two brothers. Define the current age of the younger brother as x years. Therefore, the current age of the older brother would be x + a certain number of years. Let's call this number y. According to the first statement, two years ago the older brother was three times the age of the younger brother, which means their ages at that time were (x - 2) and (x + y - 2), respectively.

According to the first statement: x + y - 2 = 3(x - 2). Consequently, we get the following equation:

x + y - 2 = 3x - 6

Now, according to the second statement regarding the future ages in three years, we get the second equation: (x + y + 3) = 2(x + 3).

By solving these two equations simultaneously:

Now substitute the value of y from the first equation into the second:

x + (2x - 4) + 3 = 2x + 6,

which simplifies to:

3x - 1 = 2x + 6,

resulting in:

x = 7.

Now find y by substituting x back into the first equation:

y = (2 * 7) - 4 = 10.

The current age of the younger brother (x) is 7 years, and the older brother (x + y) is 17 years old.

Answer 2

One brother says of his younger brother: “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 they each now?

Step-by-step explanation:

Let us suppose two years ago my brother's age was x years

Then, my age was 3x

Three years from now, my brother's age will be (x +2+3) = (x+5) years

And my age will be (3x+2+3) = (3x+5) years

But it is given that i will be twice as old as my brother.

So, 2(x+5)= (3x+5)

or, x= 5 years

So my brother's present age is 5+2= 7 years

And my age is 5*3+2= 17 years