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?
The difference between three-fifths full and one-sixth full is $\frac{3}{5}-\frac{1}{6}=\frac{13}{30}$ of the tank's capacity.  Let $x$ be the capacity of the tank in gallons.  Since $\frac{13}{30}$ of the tank's capacity is 130 gallons, we have $\frac{13}{30}x = 130$.  Multiplying both sides by $\frac{30}{13}$ gives $x = 300$, so the capacity is $\boxed{300}$ gallons.
300
Level 4
Prealgebra
Problem: 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?
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>Let the total capacity of the tank be denoted as \( x \) gallons. 

When the tank is one-sixth full, the volume of water in the tank is \( \frac{1}{6}x \) gallons. 

After adding 130 gallons, the tank becomes three-fifths full. The volume of water in the tank at this point is \( \frac{3}{5}x \) gallons. 

We can set up the equation based on the information given:

\[
\frac{1}{6}x + 130 = \frac{3}{5}x
\]

To solve for \( x \), first, we need to eliminate the fractions. We can find a common denominator, which is 30. 

Multiplying the entire equation by 30 gives:

\[
30 \left( \frac{1}{6}x \right) + 30(130) = 30 \left( \frac{3}{5}x \right)
\]

This simplifies to:

\[
5x + 3900 = 18x
\]

Next, we isolate \( x \) by moving all terms involving \( x \) to one side:

\[
3900 = 18x - 5x
\]

This simplifies to:

\[
3900 = 13x
\]

Now, we solve for \( x \):

\[
x = \frac{3900}{13}
\]

Calculating this gives:

\[
x = 300
\]

Thus, the total capacity of the tank when it is completely full is 300 gallons.<|END_OF_LATENT|> The final answer is $300$.