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Let Sue's age be \( s \). Then Jenny's age can be expressed as:
\[
j = 2s + 8
\]
According to the problem, the sum of their ages is less than 32, which gives us the inequality:
\[
s + j < 32
\]
Substituting \( j \) into the inequality, we get:
\[
s + (2s + 8) < 32
\]
Simplifying this, we have:
\[
3s + 8 < 32
\]
Subtracting 8 from both sides:
\[
3s < 24
\]
Dividing both sides by 3:
\[
s < 8
\]
Since \( s \) must be a whole number, the greatest possible age for Sue that satisfies this inequality is \( 7 \).
Thus, the greatest age that Sue could be is:
\[
\boxed{7}
\]