Gasoline gauge on a van initially read 1/4 full. when 10 gallons are added the gauge reads 3/4 full. how many more gallons for a full tank

You need 5 more gallons for a full tank. 
Since it takes 10 gallons to increase the gauge from 1/4 to 3/4 (change of 2/4 which is the same as 1/2), it must have taken 10 gallons to fill up to halfway for the tank.  
Thus the full amount would be 10*2 = 20 gallons
However, since there is already 3/4 gasoline in the tank, we only need an extra 1/4 of 20 for it to be full. 
So, 20*1/4 = 5
We need to add 5 gallons for a full tank.