Sara is 24 years younger than Joe. Six years ago she was half as old as he was. How old is he now?
present age:
Joe --- x
Sara --- x-24
Six years ago:
Joe ---- x-6
Sara --- x-24 - 6 = x - 30
x - 30 = (1/2)(x-6)
times 2
2x - 60 = x - 6
x = 54
Joe is now 54 , and Sara is now 30
check:
six years ago , Joe was 48 , and Sara was 24
Was he twice as old as Sara ??? YES
To solve this problem, we can start by setting up equations based on the given information.
Let's assume Joe's current age is represented by the variable "j" and Sara's current age is represented by the variable "s."
We are told that Sara is 24 years younger than Joe, so this can be expressed as:
s = j - 24 (Equation 1)
We are also told that six years ago, Sara was half as old as Joe, so we can set up another equation:
(s - 6) = (1/2)(j - 6) (Equation 2)
Now we can solve these equations to find Joe's current age.
First, let's substitute the value of "s" from Equation 1 into Equation 2 to eliminate "s":
(j - 24 - 6) = (1/2)(j - 6)
Expand and simplify:
j - 30 = (1/2)j - 3
Multiply through by 2 to eliminate the fraction:
2j - 60 = j - 6
Now, subtract "j" from both sides and add 60 to both sides to isolate the variable "j":
2j - j = -6 + 60
j = 54
Therefore, Joe is currently 54 years old.