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The problem states that Mr. Gilberto saves $\frac{6}{7}$ of his monthly salary. His savings increase to $5436 after his salary is increased by $376.

We are tasked with determining Mr. Gilberto's original monthly salary before the increase.

### Let's break this down:

1. Let $ x $ be Mr. Gilberto's original monthly salary.
2. The amount he saves from this salary is $\frac{6}{7} \times x$.
3. After a $376 increase, his new salary becomes $ x + 376 $, and his new savings become $5436.
4. The new savings should be $\frac{6}{7}$ of the increased salary, so:
   \[
   \frac{6}{7}(x + 376) = 5436
   \]
5. Now, we can solve for $ x $, the original salary.

Let me compute that.Mr. Gilberto's original monthly salary before the increase was $5,966.

Would you like a detailed explanation of the steps involved, or do you have any further questions?

Here are 5 related questions to expand on this concept:
1. What would Mr. Gilberto's new salary be after the increase?
2. If he saved $\frac{5}{7}$ of his salary instead, how would that affect his savings?
3. What percentage of his salary does Mr. Gilberto save, and how would that change if the fraction were different?
4. If his salary were decreased instead of increased by $376, what would his savings be?
5. How can we express the amount of money Mr. Gilberto does **not** save in terms of his salary?

**Tip:** When dealing with fractional savings, it's helpful to express the problem in terms of equations early, as it simplifies solving for unknowns!

Mr. Gilberto always saves 6/7 of his monthly salary. If his monthly salary is increased by $376, his monthly savings will be $5436. How much is Mr. Gilberto's monthly salary before the increase?

Learn how to solve for Mr. Gilberto's original salary before an increase, given that he saves 6/7 of his income. This problem involves algebra and proportional relationships, suitable for students in Grades 8-10.

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