A coffee shop creates its house brand by mixing $8 / 13$ of locally produced coffee and $5 / 13$ of imported coffee. Among the imported coffee, $3 / 5$ is from Latin America and $1 / 3$ of this Latin American Coffee is from Costa Rica. Let $x$ represent the amount of Costa Rican coffee used in the house brand, then Local coffee used in the same brand can be represented by (Note that the coffee shop is not in Latin America)
a. $20 x$
b. $12 x$
c. $4 x$
d. $16 x$
e. $8 x$
Answer
Final Answer: \(\boxed{8x}\)
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: \(\boxed{8x}\)
