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neonofarm [45]
1 year ago
10

How many gallons each of 30% alcohol and 5% alcohol should be mixed to obtain 25gal of 25% alcohol?

Mathematics
1 answer:
lozanna [386]1 year ago
4 0

Let x be the amount of the 30% alcohol and let y be the amount of 5% alcohol.

We want the total amount to by 25 gal, then we have:

x+y=25

We also want the resulting mix to be 25% alcohol, this is 0.25 in decimal form; also we know that the first type of alcohol is 30% and the second is 5%, then we have:

\begin{gathered} 0.3x+0.05y=0.25(25) \\ 0.3x+0.05y=6.25 \end{gathered}

Hence we have the system of equations:

\begin{gathered} x+y=25 \\ 0.3x+0.05y=6.25 \end{gathered}

To solve the system we solve the first equation for y:

y=25-x

then we plug this value of y in the second equation:

\begin{gathered} 0.3x+0.05(25-x)=6.25 \\ 0.3x+1.25-0.05x=6.25 \\ 0.25x=6.25-1.25 \\ 0.25x=5 \\ x=\frac{5}{0.25} \\ x=20 \end{gathered}

Once we have the value of x we plug it in the expression we found for y:

\begin{gathered} y=25-20 \\ y=5 \end{gathered}

Therefore, the mixture will have 20 gallons of 30% alcohol and 5 gallons of 5% alcohol.

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