Jimmy is 8 years old and Beth is 10 years old.
Jimmy is 8 years old and Beth is 10 years old.Let's denote Jimmy's current age as \( J \) and Beth's current age as \( B \).
According to the given information:
1. Beth is 2 years older than Jimmy: \( B = J + 2 \)
2. In 3 years, the sum of their ages will be twice as much as the sum of their ages 3 years ago:
\( (J + 3) + (B + 3) = 2 \times [(J - 3) + (B - 3)] \)
Simplifying this equation gives:
\( J + B + 6 = 2 \times (J + B - 6) \)
\( J + B + 6 = 2J + 2B - 12 \)
\( J + B = 18 \)
Now, substituting the value of \( B \) from the first equation into this equation:
\( J + (J + 2) = 18 \)
\( 2J + 2 = 18 \)
\( 2J = 16 \)
\( J = 8 \)
So, Jimmy is 8 years old, and Beth is \( 8 + 2 = 10 \) years old.
