The number of gallons of fuel used on a trip varies directly with the number of miles traveled. If a trip of 270 miles required 12 gallons of fuel, how many gallons are required for a trip of 400 miles?
Mathematics · Middle School · Thu Feb 04 2021
Answered on
To solve problems involving direct variation, you can use the formula y = kx, where y is the number of gallons of fuel used, x is the number of miles traveled, and k is the constant of variation.
First, we need to find the constant of variation (k) using the information given:
270 miles require 12 gallons of fuel. So, we can write the equation as: 12 gallons = k * 270 miles
Now, solve for k: k = 12 gallons / 270 miles k = 1/22.5 k = 0.0444 gallons/mile (approximately)
Next, use this constant of variation to find out how many gallons are needed for a trip of 400 miles: y = k * 400 miles y = 0.0444 gallons/mile * 400 miles y = 17.76 gallons
Therefore, approximately 17.76 gallons of fuel are required for a trip of 400 miles.