kristyn is 4 years younger than mario. 3 years from now, she will be two thirds as old as mario. find their present age.
k = Kristyn
m = Mario
k = m -4
(k + 3)= 2/3(m + 2)
Substitute the value of k in the second equation.
m - 4 + 3 = 2/3m + 4/3
m - 1 = 2/3m + 4/3
ELIMINATE FRACTION BY MULTIPLYING THE EQUATION BY 3.
3(m - 1) = 3(2/3m + 4/3)
3m - 3 = 2m + 4
3m - 2m - 3 + 3 = 2m - 2m + 4 + 3
m = 7
Now put the value of m in the first equation. Or you can subtract 4 from 7.
k = 7 - 4
k = 3
Kristyn is 3
Mario is 7
To solve this problem, let's use algebraic expressions to represent the ages of Kristyn and Mario.
Let's say Kristyn's present age is K years, and Mario's present age is M years.
From the given information, we know that Kristyn is 4 years younger than Mario, so we can write an equation:
K = M - 4 ... (Equation 1)
Additionally, it is stated that three years from now, Kristyn will be two-thirds of Mario's age. So, in three years, Kristyn will be (K + 3) years old, and Mario will be (M + 3) years old. We can write another equation based on this:
K + 3 = (2/3)(M + 3) ... (Equation 2)
Now, we have a system of two equations with two variables. We can solve these equations simultaneously to find the values of K and M.
First, let's substitute the value of K from Equation 1 into Equation 2:
M - 4 + 3 = (2/3)(M + 3)
Simplify the equation:
M - 1 = (2/3)(M + 3)
Multiply both sides of the equation by 3 to eliminate the fraction:
3(M - 1) = 2(M + 3)
Expand the equation:
3M - 3 = 2M + 6
Combine like terms:
3M - 2M = 6 + 3
M = 9
Now, we found that M, which represents Mario's present age, is 9 years old.
To find Kristyn's present age, we can substitute this value back into Equation 1:
K = M - 4
K = 9 - 4
K = 5
Therefore, Kristyn's present age is 5 years old and Mario's present age is 9 years old.