Answer:
24 gallons
Step-by-step explanation:
To answer this question let's call "a" the capacity of the tank in gallons.
Initially it is one third of its capacity, but when 4 gallons are added, it is half full.
This statement can be written as an equation in the following way:
[tex]\frac{1}{3}a+4=\frac{1}{2}a\\[/tex] (1)
This equation represents the given conditions, therefore solving it we can clear "a" the capacity of the tank in gallons
Solving the equation we have:
[tex]\frac{1}{3}a-\frac{1}{2}a =-4\\a (\frac{1}{3}-\frac{1}{2}) = -4\\a (-\frac{1}{6}) = -4\\a (\frac{1}{6}) = 4\\a = 24\\[/tex]
Therefore the capacity of the tank is 24 gallons.
We can check this result by verifying if it meets the given conditions. The half of 24 is 12. Therefore, if we divide 24 at 3 and then add 4, we should get half the capacity of the tank, that is, 12 gallons.
[tex]\frac{24}{3} = 8\\8 + 4 = 12[/tex]
12 is half the capacity of the tank, then equation (1) is met and the result is checked
