Given that the chemistry teacher needs to mix a 20% salt solution with an 80% salt solution to make 15 quarts of a 40% salt solution.
Let be "x" the number of quarts of 20% salt solution the teacher should mix to get the desired result, and "y" the number of quarts of 80% salt solution the teacher should mix to get the desired result.
You can write the following System of Equations using the information provided in the exercise:
[tex]\begin{cases}0.2x+0.8y={(0.4)(15)} \\ x+y=15\end{cases}[/tex][tex]\begin{cases}0.2x+0.8y={6} \\ x+y=15\end{cases}[/tex]In order to solve the exercise, you can use the Substitution Method:
1. Solve the second equation for "y":
[tex]y=15-x[/tex]2. Substitute the new equation into the first equation and solve for "x":
[tex]0.2x+0.8(15-x)=6[/tex][tex]0.2x+12-0.8x=6[/tex][tex]\begin{gathered} x=\frac{-6}{-0.6} \\ \\ x=10 \end{gathered}[/tex]3. Substitute the value into the second original equation and solve for "y":
[tex]\begin{gathered} 10+y=15 \\ y=15-10 \\ y=5 \end{gathered}[/tex]Hence, the answer is:
• 20% salt solution:
[tex]10\text{ }qt[/tex]• 80% salt solution:
[tex]5\text{ }qt[/tex]
