Question

The gasoline gauge on a van initially read 1/3 full. When 10gallons were added to the tank, the gauge read 3/4 full. How many more gallons are needed to fill the tank?

Answer 1

So it went from 1/3 full to 3/4 full when 10 gallons were put in, so.... what fraction is 10 gallons anyway? let's check the difference.

if say, when full is "x" gallons, 

$\bf \cfrac{3}{4}x-\cfrac{1}{3}x=10\implies \cfrac{9x-4x}{12}=10\implies \cfrac{5x}{12}=10\implies 5x=120 \\\\\\ x=\cfrac{120}{5}\implies x=24$