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Let's define variables to solve the problem step by step.

Let:
- $ K $ be the amount Ken invests.
- Martina's investment is described as $ \frac{4}{5} $ of Ken's investment minus $2075. So, Martina's investment can be written as $ M = \frac{4}{5}K - 2075 $.

The total partnership value is given as $88,312, so:

\[
K + M = 88,312
\]

Substitute $ M = \frac{4}{5}K - 2075 $ into the equation:

\[
K + \left( \frac{4}{5}K - 2075 \right) = 88,312
\]

Simplify and solve for $ K $:

\[
K + \frac{4}{5}K - 2075 = 88,312
\]

First, eliminate the parentheses:

\[
K + \frac{4}{5}K = 88,312 + 2075
\]

Combine like terms:

\[
K + \frac{4}{5}K = 90,387
\]

\[
\frac{5}{5}K + \frac{4}{5}K = 90,387
\]

\[
\frac{9}{5}K = 90,387
\]

Now, solve for $ K $:

\[
K = 90,387 \times \frac{5}{9}
\]

\[
K = 50,215
\]

Now that we know Ken's investment is $50,215, we can find Martina's investment:

\[
M = \frac{4}{5} \times 50,215 - 2075
\]

\[
M = 40,172 - 2075
\]

\[
M = 38,097
\]

Thus:
- Ken invested **$50,215**.
- Martina invested **$38,097**.

Would you like more details on any part of this solution?

Here are some related questions to explore further:

1. What would happen if Martina’s investment formula changed to $ \frac{3}{4} $ of Ken's investment instead?
2. How would the equation change if Martina’s deduction was $2500 instead of $2075?
3. How can you generalize this partnership model to any other total partnership value?
4. What if Ken's investment was a fixed amount of $55,000 instead of being calculated?
5. How does this partnership model reflect real-world investment agreements?

**Tip**: When dealing with word problems, defining clear variables and translating relationships into equations is key to simplifying complex scenarios!

Ken and Martina agreed to form a partnership. The partnership agreement requires that Martina invest $2075 less than four-fifths of what Ken is to invest. If the total partnership value is $88,312, how much did each partner invest?

Learn how to calculate Ken and Martina's partnership investment where Martina invests $2075 less than four-fifths of Ken's investment. The total partnership value is $88,312. This problem explores algebraic equations and proportional relationships.

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