Budgeting for a Trip: Amount Spent on Food

A college student is planning a trip and must budget for food, travel, and accommodation. The total budget for the trip is $600. Let $x$ be the amount spent on food and $y$ be the amount spent on travel. The student plans to spend twice as much on travel as on food. Additionally, the student has decided to allocate $120 for accommodation.

Set up the system of equations based on the information provided, then solve for the amount that can be spent on food. Express your answer as a decimal rounded to two decimal places.

Use the following equations to describe the situation:

1. $$ x + 2x + 120 = 600 $$

2. Solve this equation for $x$.