Question

Kevin is 3 years older than Daniel. Two years ago, Kevin was 4 times as old as Daniel.

Answer 1

Let, the age of Daniel be x years and Kevin be y years.

Given, Kevin is 3 years older than Daniel.

So we can write the equation as y=x+3

Also given, 2 years ago Kevin was 4 times as old as Daniel.

2 years ago, Daniel's age = (x-2) years

2 years ago, Kevin's age = (y-2) years.

So we can write the equation as (y-2) = 4(x-2)

We have got the two equations

y = x+3 ..... equation 1

(y-2) = 4(x-2) ..... equation 2

Now we are plugging in the value of y from equation 1 to equation 2

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

x+1 = 4(x-2)

Now we have to distribute 4 in the right side.

x+1 = 4x -8

We will have to take x in one side. so let's move 4x to the left side by subtracting it to both sides.

x -4x+1 = 4x-4x -8

-3x+1 = 0-8

-3x+1 = -8

Now we have to move 1 to the right side by subtracting 1 from both sides.

-3x +1 -1 = -8-1

-3x+0 = -9

-3x = -9

Now we can get x by moving -3 to the right side. As -3 is multiplied there so we can move it by dividing both sides by -3.

-3x/-3 = -9/-3

x = 3

So we have got the required answer. Daniel is 3 years old.