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

Rewriting the given values with common denominator:

we get:

1/3 = 4/12

3/4 = 9/12

4/12 + 10 gallons = 9/12

Which means:

10 gallons = 9/12 - 4/12

= 5/12

4/12 + 5/12 (10 Gallons) = 9/12

Since 5 = 10, 1 will be equal to 2 gallons.

There are 3 parts that need to be filled, that means 3*2 = 6 gallons. Thus 9/12 + 3/12 (6 Gallons) = 12/12 or 1 whole.