1. **State the problem:** We are given the proportion $\frac{14}{9} = \frac{56}{n} = \frac{p}{27}$ and need to find the values of $n$ and $p$. 2. **Use the property of proportions:** If $\frac{a}{b} = \frac{c}{d}$, then $a \times d = b \times c$. 3. **Find $n$ using $\frac{14}{9} = \frac{56}{n}$:** $$14 \times n = 9 \times 56$$ $$14n = 504$$ Divide both sides by 14: $$\cancel{14}n = \frac{504}{\cancel{14}}$$ $$n = 36$$ 4. **Find $p$ using $\frac{14}{9} = \frac{p}{27}$:** $$14 \times 27 = 9 \times p$$ $$378 = 9p$$ Divide both sides by 9: $$\cancel{9} \times 42 = \frac{378}{\cancel{9}}$$ $$p = 42$$ 5. **Final answer:** $$n = 36, \quad p = 42$$