A car travels miles using gallons of gasoline. At this rate, how many gallons of gasoline are needed for the car to travel miles?
For this type of rate question, first convert the given information into a clear unit rate (like miles per gallon) by dividing the total amount by the number of units. Then use that rate to scale up or down: either divide the new total by the unit rate or set up a proportion such as and solve for . Always check that your answer makes sense by estimating—if the distance is about 3 times larger, the fuel should be about 3 times as much.
Hints
Identify the rate
You are told how far the car goes using 5 gallons. How can you turn this into a “miles per gallon” rate?
Use a unit rate or a proportion
Once you know how many miles the car travels per gallon, how can you use that to find how many gallons are needed for 420 miles?
Check with proportional reasoning
Compare 420 miles to 150 miles: Is it more or less than 3 times as far? About how many times greater should the gallons be compared to 5?
Desmos Guide
Find the miles-per-gallon rate
In Desmos, type 150/5 and note the value; this is the car’s miles per gallon.
Compute the gallons needed for 420 miles
In a new line, type 420 / (150/5). The numerical result shown by Desmos is the number of gallons needed for the 420-mile trip.
Step-by-step Explanation
Find the unit rate (miles per gallon)
The car travels 150 miles using 5 gallons.
Compute miles per gallon:
So the car travels 30 miles for each gallon of gasoline.
Use the unit rate to find gallons for 420 miles
We want to know how many gallons are needed for 420 miles if the car goes 30 miles per gallon.
Set up:
Now divide 420 by 30.
Compute and choose the matching answer
Calculate:
So the car needs 14 gallons of gasoline to travel 420 miles. The correct answer is 14 (Choice B).