kristyn is 4 yrs younger than mario.three years from now she will be two thirds as old as mario. find the present age
NOW:
Mario --- x
Kristyn --- x-4
3years from now:
Mario ---- x+3
Kristyn--- x-1
"Three years from now, she will be 2/3 Mario's age"
----> (x-1) = (2/3)(x+3)
3x-3 = 2x+6
x=0
So now Mario is 9 and Krystyn is 5
check out both conditions stated, it works
Well, let's break it down:
If Mario is X years old, then Kristyn is X - 4 years old.
Three years from now, Mario will be X + 3 years old, and Kristyn will be X - 4 + 3 years old. According to the statement, Kristyn will be two-thirds the age of Mario at that time.
So, we can set up the equation: X - 4 + 3 = (2/3)(X + 3).
Now, let's solve the equation:
X - 1 = (2/3)(X + 3).
Multiply both sides of the equation by 3 to get rid of the fraction:
3(X - 1) = 2(X + 3).
Distribute the multiplication:
3X - 3 = 2X + 6.
Move all the terms with X to one side:
3X - 2X = 6 + 3.
Simplify:
X = 9.
Therefore, Mario is 9 years old.
And since Kristyn is 4 years younger, she is:
9 - 4 = 5 years old.
So, Mario is currently 9 years old, and Kristyn is currently 5 years old.
Now, wasn't that a-musing?
Let's denote Kristyn's present age as K and Mario's present age as M.
From the given information, we can establish two equations:
1) K = M - 4 (Kristyn is 4 years younger than Mario)
2) K + 3 = (2/3)(M + 3) (Three years from now, Kristyn will be two-thirds as old as Mario)
To solve these equations, we can substitute equation 1 into equation 2:
M - 4 + 3 = (2/3)(M + 3)
M - 1 = (2/3)(M + 3)
Multiplying both sides by 3 to eliminate the fraction:
3(M - 1) = 2(M + 3)
3M - 3 = 2M + 6
3M - 2M = 6 + 3
M = 9
Now that we know Mario's present age is 9, we can substitute it back into equation 1 to find Kristyn's age:
K = 9 - 4
K = 5
Therefore, Mario's present age is 9 and Kristyn's present age is 5.
To find the present age of Kristyn and Mario, let's set up equations based on the information given:
Let's assume Mario's present age is represented by x.
So, Kristyn's present age will be x - 4, as she is 4 years younger than Mario.
Three years from now, Mario's age will be x + 3, and Kristyn's age will be (x - 4) + 3 = x - 1.
According to the problem, three years from now, Kristyn will be two-thirds as old as Mario. So, we can set up the equation:
(x - 1) = (2/3)(x + 3)
Now, let's solve for x:
Multiplying both sides of the equation by 3 to get rid of the fraction:
3(x - 1) = 2(x + 3)
3x - 3 = 2x + 6
Combining like terms:
3x - 2x = 6 + 3
x = 9
Therefore, Mario's present age is 9 years old.
And, Kristyn's present age is x - 4 = 9 - 4 = 5 years old.