Question

Your car can drive 450 miles on a tank of 30 gallons.How far can it drive on 40 gallons? Round your answer to the nearest mile.How many gallons are needed to drive 960 miles? Round your answer to the nearest tenth of a gallon.

Answer 1

Hello there. To solve this question, we'll have to remember some properties about ratios.

If a car can drive 450 miles on a tank of 30 gallons, we have to determine how far can it drive on 40 gallons.

Assuming these values varies directly, then we have that

Let x be the distance that can be travelled with 40 gallons, such that

`(450)/(30)=(x)/(40)`

Simplify the fraction on the LHS by a factor of 30

`15=(x)/(40)`

Multiply both sides of the equation by a factor of 40

`x=600\text{ miles}`

Now, we have to find how many gallons are needed to drive 960 miles.

Using the same values we found, say y is the number of gallons needed to drive 960 miles, such that

`(450)/(30)=(960)/(y)`

Simplifying the fraction

`15=(960)/(y)`

Cross multiply the values, such that

`15y=960`

Divide both sides of the equation by a factor of 15

`y=64`

So the car needs 64 gallons in order to drive 960 miles.