Chris conjectures that if he accepts the promotion which is offered to him, he should be able to save enough money within 6 months to buy a new laptop. His new hourly wage will be $10.50 plus a one-time bonus of $300 paid at the time of joining. Chris is not able to work for more than 40 hours per month because of his school. If the laptop costs $400 and Chris has a car payment of $300 per month and has to spend $100 per month on gas, will he be able to save sufficient money to buy the laptop within the estimated time frame? Use a mathematical argument to support your answer.