Sara is 24 years younger than Joe. Six years ago she was half as old as he was. How old is each now?

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To solve this problem, we can use algebraic equations. Let's assign variables to the ages of Sara and Joe.

Let's say Sara's age is 's' and Joe's age is 'j'.

According to the given information, Sara is 24 years younger than Joe, so we can write the equation:

s = j - 24 -- Equation 1

Six years ago means that we need to subtract 6 from their current ages. At that time, Sara was half as old as Joe, so we can write the equation:

(s - 6) = (j - 6) / 2 -- Equation 2

Now that we have two equations (Equation 1 and Equation 2), we can solve them simultaneously to find the ages of Sara and Joe.

First, let's rewrite Equation 1 to express j in terms of s:

j = s + 24

Now substitute this expression for j in Equation 2:

(s - 6) = [(s + 24) - 6] / 2

Simplify the equation:

2(s - 6) = (s + 18)

Distribute and simplify further:

2s - 12 = s + 18

Move all the terms involving 's' to one side of the equation:

2s - s = 18 + 12

We get:

s = 30

Now substitute the value of s back into Equation 1 to find j:

j = s + 24 = 30 + 24 = 54

So, Sara is 30 years old, and Joe is 54 years old.