in june, mr tan saved 20% of his salary. In july, his monthly salary increased by $600 and he saved 15% of his new monthly salary. given that mr tan saved the same amount of money in both months, fine the percentage increase in mr tan's salary.

Let Mr. Tan's salary in June be denoted as $ x $.

### Step 1: Determine Mr. Tan's savings in June
In June, Mr. Tan saved 20% of his salary. So, the amount he saved in June is:
\[
\text{Savings in June} = 0.20x
\]

### Step 2: Determine Mr. Tan's salary in July
In July, his salary increased by $600, so his new salary in July is:
\[
\text{New salary in July} = x + 600
\]

### Step 3: Determine Mr. Tan's savings in July
In July, Mr. Tan saved 15% of his new salary. So, the amount he saved in July is:
\[
\text{Savings in July} = 0.15(x + 600)
\]

### Step 4: Set the savings in both months equal
Since the amount saved in both months is the same, we equate the savings in June and July:
\[
0.20x = 0.15(x + 600)
\]

### Step 5: Solve for $ x $
Now, solve the equation for $ x $:

\[
0.20x = 0.15x + 90
\]
\[
0.20x - 0.15x = 90
\]
\[
0.05x = 90
\]
\[
x = \frac{90}{0.05} = 1800
\]

So, Mr. Tan's salary in June was $1800.

### Step 6: Calculate the salary in July
The new salary in July is:
\[
x + 600 = 1800 + 600 = 2400
\]

### Step 7: Calculate the percentage increase in salary
The percentage increase in salary is:
\[
\text{Percentage increase} = \frac{\text{Increase in salary}}{\text{Original salary}} \times 100 = \frac{600}{1800} \times 100 = 33.33\%
\]

Thus, the percentage increase in Mr. Tan's salary is $ \boxed{33.33\%} $.

Would you like further details or explanations? Here are 5 related questions to expand your understanding:

1. If Mr. Tan’s July salary increased by $800 instead of $600, how would that affect the percentage increase?
2. What would happen if Mr. Tan saved 25% of his salary in June instead?
3. How much total money did Mr. Tan save across both months?
4. What if Mr. Tan’s salary had decreased in July? How would you calculate that?
5. How much would Mr. Tan save in July if his salary increased by 50% instead?

**Tip:** When solving percentage problems, carefully set up your equations based on the relationships between the variables for clearer results!

In June, Mr. Tan saved 20% of his salary. In July, his monthly salary increased by $600 and he saved 15% of his new monthly salary. Given that Mr. Tan saved the same amount of money in both months, find the percentage increase in Mr. Tan's salary.

Explore how to calculate the percentage increase in Mr. Tan's salary when his salary increased by $600, and he saved the same amount across two months. This problem involves algebraic concepts like percentage and linear equations, suitable for students in Grades 8-10.

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