Amy bought and then sold $15 n$ avocados, for some positive integer $n$. She made a profit of $\$ 100$. (Her profit is the difference between the total amount that she earned by selling the avocados and the total amount that she spent in buying the avocados.) She paid $\$ 2$ for every 3 avocados. She sold every 5 avocados for $\$ 4$. What is the value of $n$ ?
(A) 100
(B) 20
(C) 50
(D) 30
(E) 8
Amy bought and then sold $15 n$ avocados.

Since she bought the avocados in groups of 3 , she bought $\frac{15 n}{3}=5 n$ groups of 3 avocados.

Since she paid $\$ 2$ for every 3 avocados, she paid $\$ 2 \times 5 n=\$ 10 n$.

Since she sold the avocados in groups of 5 , she sold $\frac{15 n}{5}=3 n$ groups of 5 avocados.

Since she sold every 5 avocados for $\$ 4$, she received $\$ 4 \times 3 n=\$ 12 n$.

In terms of $n$, Amy's profit is $\$ 12 n-\$ 10 n=\$ 2 n$.

Since we know that Amy's profit was $\$ 100$, we get $\$ 2 n=\$ 100$ and so $2 n=100$ or $n=50$.