Aris is twice as old as Rico while Jay is 24 years younger than Aris. If 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, then what is their ages before and now.
Let A = Aris' age
Let R = Rico's age
Let J = Jay's age
From the problem,
Aris is twice as old as Rico:
A = 2R
Jay is 24 years younger than Aris:
J = A - 24
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
(1/2)(A - 6) = (1/2)(R + 4 + J) - 3
You have an equation for A and J (the first two equations above). You can substitute it to the third equation to solve for R. After solving for R, solve for the rest.
Hope this helps~ `u`
45
Let's assign variables to each person's age.
Let Aris's age be A, Rico's age be R, and Jay's age be J.
From the given information, we can set up the following equations:
1) A = 2R (Aris is twice as old as Rico)
2) J = A - 24 (Jay is 24 years younger than Aris)
Now let's focus on the second part of 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.
To express this algebraically, we can translate the sentence into an equation:
[(A - 6) / 2] = [(R + 4 + J) / 2 - 3]
Simplifying this equation, we get:
(A - 6) = (R + 4 + J) - 6
Substituting the values of A and J from equations 1) and 2), we have:
2R - 6 = (R + 4 + (2R - 24)) - 6
Simplifying further, we get:
2R - 6 = 3R - 22
Combining like terms, we have:
2R - 3R = -22 + 6
-R = -16
Dividing both sides by -1, we get:
R = 16
Now, substituting R = 16 into equation 1), we find:
A = 2R = 2 * 16 = 32
From equation 2), we find:
J = A - 24 = 32 - 24 = 8
Therefore, Aris is currently 32 years old, Rico is currently 16 years old, and Jay is currently 8 years old.
To solve this problem, let's work step by step.
Step 1: Set up the information given in the problem:
Let's assign variables to each person's age:
- Let Aris' age be A
- Let Rico's age be R
- Let Jay's age be J
From the given information, we have the following:
- Aris is twice as old as Rico: A = 2R
- Jay is 24 years younger than Aris: J = A - 24
Step 2: Translate the additional information into equations:
The 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" can be converted into an equation.
Taking each part of the sentence:
- "half of Aris' age six years ago" can be written as (A - 6) / 2
- "one half the sum of Rico's age in four years and Jay's present age" can be written as (R + 4 + J) / 2
Now, we can write the equation:
(A - 6) / 2 = (R + 4 + J) / 2 - 3
Step 3: Simplify and solve the equation:
Let's substitute the values we know:
From step 1, we know A = 2R and J = A - 24.
Substituting these values into the equation, we get:
(2R - 6) / 2 = (R + 4 + (2R - 24)) / 2 - 3
Simplifying further:
(R - 6) = (R + 4 + 2R - 24) - 6
R - 6 = 3R - 26 - 6
R - 6 = 3R - 32
Bringing like-terms together:
R - 3R = -6 + 32
-2R = 26
R = -26 / -2
R = 13
Now that we have Rico's age, we can find Aris' age using A = 2R:
A = 2 * 13
A = 26
Lastly, we can find Jay's age using J = A - 24:
J = 26 - 24
J = 2
So, the ages of Aris, Rico, and Jay are:
Before:
- Aris: 26 years old
- Rico: 13 years old
- Jay: 2 years old
Now:
- Aris: 32 years old
- Rico: 19 years old
- Jay: 8 years old