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Let’s go through the problem and the solution that you’ve started. Here’s what I see:

### Problem Statement:
Gopal and Henry were paid a total of $3850 for a job they did. The two parts of the problem are:

**(a)** How much was Gopal paid for the job if he was paid $2030 more than Henry?

**(b)** Gopal and Henry were paid based on the number of days they worked. Gopal worked 3 times as many days as Henry, and Gopal was paid $5 more per day than Henry. The task is to find how many days Gopal worked.

---

### Breakdown of the solution:

#### (a) How much was Gopal paid?

Let’s assume Henry was paid **H** dollars.

- Gopal was paid **H + 2030** dollars.
- Total payment: $ H + (H + 2030) = 3850 $

Solving for **H**:

\[
2H + 2030 = 3850
\]
\[
2H = 3850 - 2030 = 1820
\]
\[
H = \frac{1820}{2} = 910
\]

So, Henry was paid $910, and Gopal was paid:

\[
910 + 2030 = 2940
\]

**Answer to (a): Gopal was paid $2940.**

#### (b) How many days did Gopal work?

- Gopal worked 3 times as many days as Henry.
- Gopal was paid $5 more per day than Henry.

Let’s assume Henry worked **d** days and was paid **p** dollars per day. Gopal, who worked 3 times as many days (i.e., $3d$), was paid **p + 5** dollars per day.

We can set up the equations based on their total earnings:

For Henry:
\[
d \times p = 910
\]

For Gopal:
\[
3d \times (p + 5) = 2940
\]

Now, let's solve this system of equations to find **d**.

I'll calculate this for you.The solution shows that Henry worked **14 days** and was paid **$65** per day. Therefore, Gopal, who worked 3 times as many days, worked:

\[
3 \times 14 = 42 \text{ days}
\]

**Answer to (b): Gopal worked 42 days.**

Would you like further details or clarifications?

Here are some related questions to expand on this:

1. How much did Henry earn per day, and what would his total pay have been if he worked the same number of days as Gopal?
2. How would the solution change if Gopal was paid $10 more per day than Henry instead of $5?
3. What if both Gopal and Henry worked the same number of days but Gopal was paid $2030 more—how would their daily rates change?
4. How would the problem change if the total payment was $5000 instead of $3850, while keeping the same pay difference?
5. Could you solve the problem if only the total days worked by both were given and not their daily pay difference?

**Tip:** When solving word problems involving ratios or multiple unknowns, it's helpful to translate the relationships into clear algebraic equations.

Gopal and Henry were paid a total of $3850 for a job they did. Gopal was paid $2030 more than Henry. (a) How much was Gopal paid for the job? (b) Gopal and Henry were paid based on the number of days they worked. Gopal worked 3 times as many days as Henry, and Gopal was paid $5 more per day than Henry. How many days did Gopal work?

Solve a two-part algebra problem where Gopal and Henry were paid $3850 in total, with Gopal earning $2030 more. Determine how much Gopal was paid and how many days he worked, given Gopal worked 3 times as many days and was paid $5 more per day than Henry.

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