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
[tex]\frac{450}{30}=\frac{x}{40}[/tex]
Simplify the fraction on the LHS by a factor of 30
[tex]15=\frac{x}{40}[/tex]
Multiply both sides of the equation by a factor of 40
[tex]x=600\text{ miles}[/tex]
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
[tex]\frac{450}{30}=\frac{960}{y}[/tex]
Simplifying the fraction
[tex]15=\frac{960}{y}[/tex]
Cross multiply the values, such that
[tex]15y=960[/tex]
Divide both sides of the equation by a factor of 15
[tex]y=64[/tex]
So the car needs 64 gallons in order to drive 960 miles.
