smc

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 $\boxed{a>9,b>6}$.