Archie is 12 years older than her brother Channie. Four years from now, Channie will be two-thirds as old as Archie. How old are they now?
To solve this problem, let's break it down step by step.
Let's assume Channie's current age is C years.
According to the given information, Archie is 12 years older than Channie, so Archie's current age is A = C + 12 years.
Four years from now, Channie will be C + 4 years old, and Archie will be A + 4 years old.
The problem states that, in four years, Channie will be two-thirds as old as Archie. Mathematically, this can be represented as:
C + 4 = (2/3) * (A + 4)
Let's substitute the earlier expressions for A and C into the equation:
C + 4 = (2/3) * (C + 12 + 4)
Now, let's simplify the equation:
C + 4 = (2/3) * (C + 16)
Multiply through by 3 to remove the fraction:
3 * (C + 4) = 2 * (C + 16)
Expand the equation:
3C + 12 = 2C + 32
Subtract 2C from both sides:
C + 12 = 32
Subtract 12 from both sides:
C = 32 - 12
C = 20
So Channie's current age is 20 years.
To find Archie's current age, we substitute the value of C back into the expression A = C + 12:
A = 20 + 12
A = 32
Therefore, Archie's current age is 32 years, and Channie's current age is 20 years.
her brother --- x
Archie ------- x+12
four years from now:
brother = x+4
Archie = x+12 + 4 = x+16
x+4 = (2/3)(x+16)
solve for x and sub into original definitions