Write a real-world problem that can be modeled by the inequality 10x > 5.5x + 31.5

Kim and Jane invested the same amount in two different types of investment plans.

After a certain period, Kim earned 10 times of what he invested and Jane earned $31.5 more than 5.5 times of the money she invested.

If Kim's earning is more than Jane's earning, find the minimum amount they invested at the beginning.

Let x be the money they invested at the beginning.

So, after a certain period,

Kim's earnings = 10x and

Jane's earnings = 5.5x + 31.5

Since Kim earned more than Jane,

10x > 5.5x + 31.5.

then