Math – Exercise 6 (Algebra)

Given

A solution with 12% alcohol (a1) and another with 26% (a2).

Find

The amount of each solution to mix 5L with 17% alcohol.

Solution


\(
\begin{align*}
a_1 + a_2 &= 5 \\
0,12a_1 + 0,26a_2 &= 0,17 \cdot 5 = 0,85 \\\\
a_1 &= 5 – a_2 \\
0,12(5 – a_2) + 0,26a_2 &= 0,85 \\
0,6 – 0,12a_2 + 0,26a_2 &= 0,85 \\
0,14a_2 &= 0,25 \\
a_2 &\approx 1,786 \\
a_1 &\approx 3,214
\end{align*}
\)

Answer

1,786L with 26% alcohol and 3,214L with 12% alcohol.