Question 969351
This is a proportion problem and is solved by cross multiplication.

3 tablespoons of salt is to 20 gallons as x tablespoons is to 50 gallons.

You know you will need more salt.  Because 50 gallons is more than double 20 gallons, you will need more than double 3 tablespoons, so the answer has to be more than 6.

(3/20)=(x/50)

Cross-multiply:  3*50=x *20
20 x = 150
x=7.5 tablespoons   The answer makes sense.  

You can also do this by recognizing that 50 is 2 and a half times 20.  Therefore, the tablespoons need to be 2 and a half times 3, or 7.5.