Noah saves 20% of his salary. If his salary decreases by 15%, his savings will decrease by $210. How much is noah's original salary?

To solve this problem, we need to determine Noah's original salary, given the information about his savings and the impact of a salary decrease. Let's go through the steps:

### Step 1: Define Variables

Let $ S $ be Noah's original salary. 

Since Noah saves 20% of his salary, his savings amount to:

\[
0.20S
\]

### Step 2: Determine Savings After Salary Decrease

If Noah's salary decreases by 15%, his new salary becomes:

\[
S - 0.15S = 0.85S
\]

Noah's savings, being 20% of his new salary, will then be:

\[
0.20 \times 0.85S = 0.17S
\]

### Step 3: Calculate the Decrease in Savings

The problem states that this decrease in savings amounts to $210. So, the decrease in savings can be expressed as:

\[
0.20S - 0.17S = 210
\]

Simplifying the left side gives:

\[
0.03S = 210
\]

### Step 4: Solve for $ S $

To find Noah's original salary, divide both sides by 0.03:

\[
S = \frac{210}{0.03} = 7000
\]

Thus, Noah's original salary is $\$7000$.

### Conclusion

Noah's original salary is **$7000**.

If you have any further questions or need more details, feel free to ask!

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Here are some related questions for further exploration:

1. What will Noah's savings be after the salary decrease?
2. If Noah decided to save 25% of his salary, how much would he save initially?
3. How much does Noah spend after his salary decreases?
4. What would Noah's savings be if his salary increased by 10% instead of decreasing?
5. If Noah saves an additional $50 per month, how much will he save in a year?
6. How much was Noah's monthly expenditure before the salary decrease?
7. What percentage of Noah's new salary is his savings after the decrease?
8. How much more does Noah need to save monthly to make up for the $210 decrease in savings?

**Tip:** When dealing with percentage changes, calculate the actual change first and use it to determine the original or new amounts based on the given percentage.

Learn how to calculate Noah's original salary when given information about his savings and a salary decrease. This problem involves percentage calculations and linear equations. Explore the step-by-step solution and related questions.

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