On a cross-country trip, a car uses 5 gallons of gas for every 120 miles it travels. How many gallons of gas does the car use if it travels 600 miles? How far can the car travel if it uses 30 gallons of gas? Make a table of equivalent ratios to help you answer the questions. Then graph the ratios. The car uses \( \square \) gallons of gas if it travels 600 miles. (Type a whole number.)

To solve the problem, let’s first find the equivalent ratios for the gas usage. The car uses 5 gallons of gas for 120 miles, which can be represented as: - 5 gallons → 120 miles - 10 gallons → 240 miles (double the amount) - 15 gallons → 360 miles (triple the amount) - 20 gallons → 480 miles (quadruple the amount) - 25 gallons → 600 miles (five times the amount) From this table, we can see that if the car travels 600 miles, it uses 25 gallons of gas. Next, to determine how far the car can travel if it uses 30 gallons, we can find the additional distance using the ratios: - 30 gallons would be 30/5 times the base ratio (6 times). Multiplying the distance of 120 miles by 6 gives us 720 miles. So, to recap: The car uses 25 gallons of gas if it travels 600 miles. The car can travel 720 miles if it uses 30 gallons of gas. Now, let’s plot those equivalent ratios on a graph with gallons on the X-axis and miles on the Y-axis. The plotted points would be (5, 120), (10, 240), (15, 360), (20, 480), (25, 600), and for 30 gallons, (30, 720), creating a nice straight line representing the relationship between gallons of gas used and miles traveled!