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A tank has a capacity of 13 gallons. When it is full, it contains 20% alcohol. How many gallons must be replaced with an 70% alcohol solution to give 13 gallons of 30% solution? Round your final answer to 1 decimal place if necessary.

Respuesta :

Given:

A tank has a capacity of 13 gallons. When it is full.

The tank contains 20% alcohol.

We will find the number of gallons that must be replaced with a 70% alcohol solution to give 13 gallons of 30% solution

Let the number of gallons that must be replaced = x

so, there are x gallons with a 70% alcohol and (13 -x) with a 20% alcohol.

So, we can write the following equation:

[tex]70x+20(13-x)=30*13[/tex]

Solve the equation to find (x):

[tex]\begin{gathered} 70x+20*13-20x=30*13 \\ 50x+260=390 \\ 50x=390-260 \\ 50x=130 \\ x=\frac{130}{50}=2.6\text{ gallons} \end{gathered}[/tex]

So, the answer will be 2.6 gallons

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