Six years ago, DJ’s mother was 8 less than twice the age of DJ then. Four years from now, twice her age will be four more than thrice his age. How old is DJ now?

Question

Six years ago, DJ’s mother was 8 less than twice the age of DJ then. Four years from now, twice her age will be four more than thrice his age. How old is DJ now?

Answer 1

To solve this problem, we can start by assigning variables to the ages mentioned in the question. Let's say DJ's current age is "x" years and DJ's mother's current age is "y" years.

According to the problem, six years ago, DJ's mother was 8 less than twice DJ's age then. So, we can set up the equation:

y - 6 = 2(x - 6) - 8

Simplifying this equation, we get:

y - 6 = 2x - 12 - 8
y - 6 = 2x - 20

Next, the problem states that four years from now, twice DJ's mother's age will be four more than thrice DJ's age. So, we can set up another equation:

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

Simplifying this equation, we get:

2y + 8 = 3x + 12 + 4
2y + 8 = 3x + 16

Now we have two equations:

y - 6 = 2x - 20
2y + 8 = 3x + 16

To solve this system of equations, we can use the method of substitution or elimination.

Let's use the elimination method:

Multiply the first equation by 2, and the second equation by -1 to cancel out the "y" term:

2y - 12 = 4x - 40
-2y - 8 = -3x - 16

Add the two equations:

-12 - 8 = 4x - 3x - 40 - 16
-20 = x - 56

Rearrange the equation:

x = -20 + 56
x = 36

Therefore, DJ's current age is 36 years.

Answer 2

six years ago:

DJ's age ---- x
his mom --- 2x - 8

Now:
DJ ---- x+6
his mom ----2x-8 + 6 = 2x - 2

4 years from now:
DJ --- x+6 + 4 = x+10
his mom --- 2x-2 + 4 = 2x + 2

2(2x+2) = 3(x+10) + 4

solve for x, then sub into x+6

Answer 3

Well, this sounds like quite a mathematical puzzle. Let me just grab my calculator... or maybe some clown shoes would be more appropriate in this situation.

Let's call DJ's age "x" now. According to the clues, we can set up some equations to solve this conundrum.

Six years ago, DJ's mother was 8 less than twice DJ's age then. So, DJ's mother's age six years ago was (2x - 8). Since we went back in time, DJ's mother's age now would be (2x - 8) + 6. Got it? Good.

Now let's move on to the second part of this mind-boggling challenge. Four years from now, twice DJ's mother's age will be four more than thrice DJ's age. So, we get the equation: 2((2x - 8) + 6 + 4) = 3(x + 4) + 4.

Now, let's simplify that equation. 2(2x + 2) = 3x + 16 + 4. This simplifies to 4x + 4 = 3x + 20.

Finally, we solve this equation like a clown who's really good at math. Subtracting 3x from both sides, we get x = 16.

So, DJ's age now is 16! Congratulations, DJ! You've officially solved the riddle of your own age.

Answer 4

Let's solve this step by step:

Step 1: Present age of DJ's mother
Let's represent DJ's current age as x.
So, six years ago, DJ's age was x-6.
According to the first sentence, DJ's mother was 8 less than twice DJ's age, so:
2(x-6) - 8 = DJ's mother's age 6 years ago.

Step 2: DJ's mother's age now
Since six years have passed, DJ's mother's age now is:
(2(x-6) - 8) + 6 = 2(x-6) - 2.

Step 3: DJ's age four years from now
DJ's age four years from now is:
x + 4.

Step 4: DJ's mother's age four years from now
According to the second sentence, four years from now, twice DJ's mother's age will be four more than thrice DJ's age.
So, we can set up the equation:
2(2(x-6) - 2) = 3(x + 4) + 4.

Step 5: Solve the equation
Now, let's solve the equation from step 4 to find DJ's current age:

2(2(x-6) - 2) = 3(x + 4) + 4.
4(x-6) - 4 = 3x + 12 + 4.
4x - 24 - 4 = 3x + 12 + 4.
4x - 28 = 3x + 16.
4x - 3x = 16 + 28.
x = 44.

Therefore, DJ is currently 44 years old.