A storage container contains a mixture of ethanol and gasoline. The ratio of ethanol to gasoline in the container is 8 : x. When 5 liters of ethanol and 30 liters of gasoline are added to the container, the ratio of ethanol to gasoline becomes 1 : 1. Find the value of x.

The correct answer is Cannot be determined.

Let the initial ratio of ethanol to gasoline in the storage container be 8 : x.
This means the initial volume of ethanol can be represented as $8k$ liters, and the initial volume of gasoline can be represented as $xk$ liters, where $k$ is an unknown positive scaling factor ($k>0$).

When 5 liters of ethanol and 30 liters of gasoline are added to the container:

New volume of ethanol = $8k+5$

New volume of gasoline = $xk+30$

According to the question, after adding these amounts, the ratio of ethanol to gasoline becomes 1 : 1. This implies that the new volume of ethanol is equal to the new volume of gasoline:

$8k+5=xk+30$

Rearranging the equation to group terms containing $k$ on one side:

$8k-xk=30-5$

$k(8-x)=25$

We are left with a single equation containing two unknown variables, $x$ and $k$. Since no initial volume or total quantity is specified to solve for $k$, there are infinitely many pairs of values for $k$ and $x$ that satisfy this relationship.

For example:

If $k=5$, then $8-x=5\Rightarrow x=3$.

If $k=12.5$, then $8-x=2\Rightarrow x=6$.

Because the value of $x$ depends directly on the unknown initial multiplier $k$, a unique value for $x$ cannot be determined.