Aris is twice as old as Rico while Jay is 24 years younger than Aris. In half of Aris' age six years ago was three less than one-half the sum of Rico's age in four years and Jay's present age, find the ages of each.
Oh boy, let's break out the ol' clown calculator and solve this puzzle with a splash of humor! Let's give it a go:
Let's assume Rico's age is "X" (because I'm an X-cellent clown bot!). That means Aris is twice as old as Rico, so Aris' age is 2X. And Jay is 24 years younger than Aris, so Jay's age is 2X - 24.
Here's the fun part: half of Aris' age six years ago, so Aris' age six years ago is 2X - 6. Meanwhile, Rico's age in four years is X + 4, and Jay's present age is 2X - 24.
According to the riddle, half of Aris' age six years ago was three less than one-half the sum of Rico's age in four years and Jay's present age. So we can write it as an equation:
(1/2)(2X - 6) = (1/2)(X + 4 + 2X - 24) - 3
Now, let's solve it (drumroll, please!):
X - 3 = (X + 4 + 2X - 24)/2 - 3
2X - 6 = 3X - 26
X = 20
Now that we know Rico's age is 20, we can find the ages of Aris and Jay:
Aris = 2X = 2 * 20 = 40
Jay = 2X - 24 = 2 * 20 - 24 = 16
So, Rico is 20 years old, Aris is 40 years old, and Jay is 16 years old. Ta-da!
Rico's age now: x
Aris' age now: 2x
Jay's age: 2x-24
six years ago Aris was 2x-6
in four years Rico's age will be x+4
(1/2)(2x-6) = (1/2)(x+4 + 2x-24) - 3
2x-6 = 3x - 20 - 6
-x = -20
x = 20
present ages:
Rico = 20
Aris = 40
Jay = 16
Let's assign variables to the ages of Aris, Rico, and Jay.
Let A be the age of Aris.
Let R be the age of Rico.
Let J be the age of Jay.
We are given the following information:
1) Aris is twice as old as Rico:
A = 2R
2) Jay is 24 years younger than Aris:
J = A - 24
3) In half of Aris' age six years ago was three less than one-half the sum of Rico's age in four years and Jay's present age:
Half of Aris' age six years ago: 0.5(A - 6)
One-half the sum of Rico's age in four years and Jay's present age: 0.5(R + 4 + J)
Based on the given information, we can now set up the equation:
0.5(A - 6) = 0.5(R + 4 + J) - 3
Let's simplify the equation:
0.5A - 3 = 0.5R + 2 + 0.5J - 3
0.5A - 0.5R - 0.5J = 2
Since we have two equations for three variables, we need another equation. We can substitute the values of A and J from the given information:
A = 2R
J = A - 24
Substituting these values into the equation:
0.5(2R) - 0.5R - 0.5(J) = 2
R - 0.5J = 2 (Equation 1)
Substituting the value of J from the second equation:
R - 0.5(A - 24) = 2
Simplifying this equation:
R - 0.5A + 12 = 2
R - 0.5A = -10 (Equation 2)
We now have a system of equations:
1) R - 0.5J = 2
2) R - 0.5A = -10
Solving this system of equations will give us the values of R and A.
To solve this problem, let's break it down into individual statements and use variables to represent the ages of each person.
Let's assume:
- Aris' age is A.
- Rico's age is R.
- Jay's age is J.
From the given information, we can form the following equations:
1) "Aris is twice as old as Rico":
A = 2R
2) "Jay is 24 years younger than Aris":
J = A - 24
Now let's analyze the second half of the problem statement: "In half of Aris' age six years ago was three less than one-half the sum of Rico's age in four years and Jay's present age."
First, consider "half of Aris' age six years ago":
Half of Aris' age six years ago = 0.5 * (A - 6)
Next, consider "one-half the sum of Rico's age in four years and Jay's present age":
Half of the sum of Rico's age in four years and Jay's present age = 0.5 * (R + 4 + J)
According to the problem statement, half of Aris' age six years ago was three less than one-half the sum of Rico's age in four years and Jay's present age. So, we can set up the equation:
0.5 * (A - 6) = 0.5 * (R + 4 + J) - 3
Now, let's substitute the values from equations (1) and (2) into this equation:
0.5 * (2R - 6) = 0.5 * (R + 4 + (A - 24)) - 3
Simplifying this equation:
R - 3 = 0.5R - 2 + 0.5A - 12 - 3
R - 3 = 0.5R + 0.5A - 17
Multiplying the entire equation by 2 to clear the decimal:
2R - 6 = R + A - 34
Substituting the value of A from equation (1) into this equation:
2R - 6 = R + 2R - 34
Combining like terms:
2R - 6 = 3R - 34
Subtracting 2R from both sides:
-R - 6 = -34
Adding 6 to both sides:
-R = -28
Multiplying both sides by -1 to solve for R:
R = 28
Now, substitute the value of R back into equation (1) to find A:
A = 2 * R = 2 * 28 = 56
Finally, substitute the value of A into equation (2) to find J:
J = A - 24 = 56 - 24 = 32
So, the ages of each person are:
- Aris is 56 years old.
- Rico is 28 years old.
- Jay is 32 years old.