The gasoline gauge on a van initially read 1/8 full. when 15 gallons were added to the tank the gauge read 3/4 full. how many more gallons are needed to fill the tank

So 15 gallons of gas brought it from 1/8 full to 3/4 full.

Let's change 3/4 to the equivalent fraction 6/8  so that the denominators are the same.    (3/4 = 6/8)

So 15 gallons of gas brought it from 1/8 to 6/8   Those 15 gallons must be 5/8 of the tank's capacity   6/8 - 1/8 = 5/8

So 15 is 5/8 of what number?  (This will tell us the capacity of the whole tank)

15 = 5/8n
Divide both sides by 5/8 (remembering to multiply by the reciprocal 8/5)
15 ÷ 5/8  = 15 x  8/5  = 18

So the tank holds 24 gallons and (since it is 3/4 full or has 18 gallons) it needs 6 gallons to fill the tank.

Check - at first  1/8 full (1/8 of 24 = 3)  So we started with 3 gallons. 15 gallons added to the 3 gallons is 18 gallons.  Now the tank is 6/8 (3/4 full).  The remaining 1/4 (2/8) of a tank is the difference between 18 and it's capacity (24 gallons)  so it will need 6 gallons to fill it up..