A tank is to be filled with water. When the tank is one-sixth full, 130 gallons of water are added, making the tank three-fifths full. How many gallons does the tank contain when it is completely full?

Guest Jun 13, 2019

#1**0 **

Let the full tank = T

Solve for T:

T/6 + 130 = (3 T)/5

Put each term in T/6 + 130 over the common denominator 6: T/6 + 130 = T/6 + 780/6:

T/6 + 780/6 = (3 T)/5

T/6 + 780/6 = (T + 780)/6:

(T + 780)/6 = (3 T)/5

Multiply both sides by 30:

(30 (T + 780))/6 = (30×3 T)/5

5 (T + 780) = (30×3 T)/5

5 (T + 780) = 6×3 T

5 (T + 780) = 18 T

Expand out terms of the left hand side:

5 T + 3900 = 18 T

-13 T = -3900

**T = 300 Gallons when the tank is full.**

Guest Jun 14, 2019