Let's denote the amount each friend receives as follows:

• Let $x$ be the amount that the second friend receives.
• The third friend gets four times the second friend's portion, so the third friend receives $4x$.
• The first friend gets twice the third friend's portion, so the first friend receives $2(4x) = 8x$.

Now, the total prize money is $195,000. Therefore, the sum of the amounts each friend receives is:

$8x + 4x + x = 195,000$

Simplifying the left side:

$13x = 195,000$

Now, solve for $x$:

$x = \frac{195,000}{13} = 15,000$

So, the second friend receives $15,000. Now, we can find how much the third and first friends receive:

• The third friend receives $4x = 4(15,000) = 60,000$.
• The first friend receives $8x = 8(15,000) = 120,000$.

Thus, the amounts each friend receives are:

• First friend: $120,000
• Second friend: $15,000
• Third friend: $60,000

Would you like further clarification or details?

Here are 5 related questions to extend your understanding:

1. What if the total prize money was $300,000? How much would each friend receive?
2. If the second friend received twice as much, how would the amounts change?
3. What fraction of the total amount does each friend receive?
4. How would you distribute the prize if the third friend got 3 times the second friend's portion instead of 4 times?
5. Can you express the first friend's amount as a fraction of the total?

Tip: When solving problems with relationships between unknowns, assigning variables carefully can simplify the entire process.