Respuesta :
Given:-
A tank has a capacity of 13 gallons. When it is full, it contains 10% alcohol.
To find how many gallons must be replaced with a 70% alcohol solution to give 13 gallons of 50% solution.
Let x denote the replaced solution containing 70 percent of alcohol.
S0 13-x contains 10% of alcohol.
Since 70 percent of alcohol contained in x. we get,
[tex](13-x)\times\frac{10}{100}+x\times\frac{70}{100}=13\times\frac{50}{100}[/tex]Now we simplify the above equation to get the required value of x. so we get,
[tex]\begin{gathered} (13-x)\frac{10}{100}+x\frac{70}{100}=13\times\frac{50}{100} \\ (13-x)\times\frac{1}{10}+x\frac{7}{10}=13\times\frac{1}{2} \\ \frac{1}{10}(13-x+7x)=\frac{13}{2} \\ \frac{1}{10}(13+6x)=\frac{13}{2} \\ 13+6x=\frac{13\times10}{2} \end{gathered}[/tex]So by further simplifications. we get,
[tex]\begin{gathered} 13+6x=\frac{13\times10}{2} \\ 13+6x=65 \\ 6x=65-13 \\ 6x=52 \\ x=\frac{52}{6} \\ x=8.666 \end{gathered}[/tex]So the required value of gallons is approximately 8.7
