Step 1 :Find the ratio of local coffee to Costa Rican coffee in the house brand. We know that \(\frac{8}{13}\) of the coffee is local and \(\frac{5}{13}\) is imported.
Step 2 :Among the imported coffee, \(\frac{3}{5}\) is from Latin America, and \(\frac{1}{3}\) of that is from Costa Rica.
Step 3 :Calculate the amount of Costa Rican coffee in the house brand: \(\frac{5}{13} \times \frac{3}{5} \times \frac{1}{3} = \frac{1}{13}\)
Step 4 :Calculate the ratio of local coffee to Costa Rican coffee: \(\frac{\frac{8}{13}}{\frac{1}{13}} = 8\)
Step 5 :Final Answer: \(\boxed{8x}\)