Three friends got the prize money worth ​$195 comma 000195,000. The first friend would get twicetwice the amount of the third​ friend's portion. The third friend would get four timesfour times the amount of the second​ friend's portion. Determine the amount that each friend would receive.
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Part 1
The first friend would get ​$enter your response here​, the second friend would get ​$enter your response here​, and third friend would get ​$enter your response here

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.

Three friends got the prize money worth ​$195,000. The first friend would get twice the amount of the third​ friend's portion. The third friend would get four times the amount of the second​ friend's portion. Determine the amount that each friend would receive.

Learn how to distribute $195,000 among three friends, where the first friend receives twice the third friend's portion, and the third friend gets four times the second friend's portion. This step-by-step algebraic solution covers linear equations and algebraic manipulation, suitable for students in Grades 6-8.

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