Shyam invested money in the stock market

Given that question: Shyam invested money in the stock market. In the first year, his stock increased 20%. He paid his stock broker $300 and then lost $450. He withdrew $500, and then his remaining investment doubled. Shyam’s investment is now worth $7100. How much was Shyam’s original investment?

The solution is as follows:

Let the amount Shyam invested in the stock market be x, then in the first year his stock increased by 20% giving 1.2x.

He paid his stockbrocker $300 to have 1.2x - $300 left, and he lost $450 to have 1.2x - $300 - $450 = 1.2x - $750 left.

He withdrew $500 to have 1.2x - $750 - $500 = 1.2x - $1,250 left.

His remaining investment doubled to have 2(1.2x - $1,250) = 2.4x - $2,500

Shyam's investment is now worth $7,100 which means that
2.4x - $2,500 = $7,100
2.4x = $7,100 + $2,500 = $9,600
x = $9,600 / 2.4 = $4,000

Therefore, the value of Shyam's original investment is $4,000

2