https://file.aiquickdraw.com/mathbot/file/1729681870844do1p4brx.jpg

The equation shown in the image is:

\[
\frac{1600 - x}{x} \times 100 + 16 = \frac{1800 - x}{x} \times 100
\]

To solve this equation, we can proceed step by step:

1. First, simplify the terms on both sides of the equation:
   \[
   \frac{1600 - x}{x} \times 100 = \frac{100(1600 - x)}{x}
   \]
   and
   \[
   \frac{1800 - x}{x} \times 100 = \frac{100(1800 - x)}{x}.
   \]

2. Now, rewrite the equation:
   \[
   \frac{100(1600 - x)}{x} + 16 = \frac{100(1800 - x)}{x}.
   \]

3. Multiply through by \(x\) to eliminate the denominators:
   \[
   100(1600 - x) + 16x = 100(1800 - x).
   \]

4. Expand both sides:
   \[
   160000 - 100x + 16x = 180000 - 100x.
   \]

5. Combine like terms:
   \[
   160000 - 84x = 180000 - 100x.
   \]

6. Rearrange to isolate \(x\):
   \[
   16x = 20000.
   \]

7. Finally, solve for \(x\):
   \[
   x = \frac{20000}{16} = 1250.
   \]

So, the solution is \(x = 1250\).

Would you like further clarification or more details on any step?

Here are 5 related questions you might want to explore:
1. What would happen if the constants 1600 and 1800 were changed?
2. How does this equation model a real-world scenario?
3. Can you generalize this type of equation for different values of constants?
4. How would this solution change if an additional term were added to one side?
5. What are the properties of the resulting equation after solving for \(x\)?

**Tip:** When dealing with fractions in equations, multiplying through by a common denominator can simplify your work early on!

Solve the equation: (1600 - x) / x * 100 + 16 = (1800 - x) / x * 100.

Learn how to solve the linear equation (1600 - x) / x * 100 + 16 = (1800 - x) / x * 100 with detailed steps. This algebraic problem involves simplifying and balancing equations, suitable for high school students in Grades 9-12.

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