Use math symbols to write an equation and an inequality based on the conditions in the problem.
\[5a+b>51\]
\[3a-b=21\]
From the second equation, $b = 3a-21$ and $a = 7 + b/3$.
Substituting $b$ in the inequality results in
\[5a + 3a - 21 > 51\]
\[8a > 72\]
\[a > 9\]
Substituting $a$ in the inequality results in
\[35 + \frac{5b}{3} + b > 51\]
\[35 + \frac{8b}{3} > 51\]
\[\frac{8b}{3} > 16\]
\[b > 6\]
The answer is $\boxed{\textbf{(A)}}$.
Five times $A$'s money added to $B$'s money is more than $$51.00$. Three times $A$'s money minus $B$'s money is $$21.00$.
If $a$ represents $A$'s money in dollars and $b$ represents $B$'s money in dollars, then:
$\textbf{(A)}\ a>9, b>6 \qquad \textbf{(B)}\ a>9, b9, b=6\qquad \textbf{(D)}\ a>9, \text{but we can put no bounds on} \text{ } b\qquad \textbf{(E)}\ 2a=3b$