six years ago, jim was four times as old as Fe. In four years, he would be twice as old as fe.How old are they now?
4 years ago:
Fe : --- x
Jim: --- 4x
Now:
Fe = x+4
Jim = 4x+4
4 years from now:
Fe = x+8
Jim = 4x + 8
4x+8 = 2(x+8)
4x + 8 = 2x + 16
2x = 8
x = 4
Now, Fe is 8 and Jim is 20
To solve this problem, let's start by representing their ages with variables. Let's assume Jim's current age is J, and Fe's current age is F.
Based on the information provided, we can create two equations:
Equation 1: "Six years ago, Jim was four times as old as Fe."
J - 6 = 4(F - 6)
Equation 2: "In four years, Jim would be twice as old as Fe."
J + 4 = 2(F + 4)
Now, we have a system of two equations in two variables. We can solve this system to find the values of J and F.
Let's start by solving Equation 1 for J:
J - 6 = 4F - 24
J = 4F - 24 + 6
J = 4F - 18
Now, substitute this value of J in Equation 2:
4F - 18 + 4 = 2(F + 4)
4F - 14 = 2F + 8
4F - 2F = 8 + 14
2F = 22
F = 11
Now that we have found Fe's current age, we can substitute this value back into Equation 1 to find Jim's current age:
J = 4F - 18
J = 4 * 11 - 18
J = 44 - 18
J = 26
Therefore, Jim's current age is 26 and Fe's current age is 11.