Finding Fuel Needed
Finding the fuel needed for a trip is a ratio and proportion problem: if a car travels a known number of miles per gallon (mpg), divide the total miles by the mpg to find gallons required. For example, driving 360 miles at 30 mpg requires 360 / 30 = 12 gallons. This 7th grade applied math skill from Saxon Math Course 2 reinforces unit rate reasoning and proportional thinking — the same framework used for budgeting, cooking, and any real-world rate calculation.
Key Concepts
Property To find how much fuel is needed for a trip, use a proportion that relates fuel efficiency (miles per gallon) to the total distance and total fuel: $$ \frac{\text{miles}}{1 \text{ gallon}} = \frac{\text{total miles}}{\text{total gallons}} $$.
Examples A car gets 30 miles per gallon. How many gallons are needed for a 360 mile trip? $$\frac{30}{1} = \frac{360}{g} \rightarrow 30g = 360 \rightarrow g = 12 \text{ gallons}$$ If a truck averages 20 miles per gallon, how much fuel is used for 500 miles? $$\frac{20}{1} = \frac{500}{g} \rightarrow 20g = 500 \rightarrow g = 25 \text{ gallons}$$.
Explanation Your car's miles per gallon (MPG) is a rate! A ratio box lets you set up a simple proportion to figure out exactly how much fuel you need for a road trip. This way, you can plan your stops and budget for gas without any guesswork.
Common Questions
How do you calculate how much fuel is needed for a trip?
Divide the total trip distance by the vehicle fuel efficiency (miles per gallon). For a 360-mile trip at 30 mpg: 360 / 30 = 12 gallons needed.
What is a unit rate and how does it apply to fuel problems?
A unit rate expresses a ratio per one unit — here, miles per one gallon. Dividing total miles by this rate gives the total gallons, which is a direct application of proportional reasoning.
How do you find fuel cost for a trip?
First find gallons needed (miles / mpg), then multiply by the price per gallon. For 12 gallons at $3.50 per gallon: 12 x $3.50 = $42 total fuel cost.
What grade covers fuel and rate problems?
Fuel and rate problems appear in 7th grade Saxon Math Course 2 as applications of ratio and proportion, connecting mathematical concepts to practical real-world contexts.
How is finding fuel needed like other proportion problems?
It uses the same structure: given a rate (mpg) and a total quantity (miles), find the missing quantity (gallons). This is identical to recipe scaling, speed-distance-time, and other proportion types.
What if you know the gallons and want to find the distance?
Multiply gallons by mpg. If you have 8 gallons and get 32 mpg, you can travel 8 x 32 = 256 miles.