Question

A chemistry teacher needs to mix a 20% salt solution with a 80% salt solution to make 15 qt of a 40% salt solution. How many quarts of each solution should the teacher mix to get the desired result?20% salt solution qt80% salt solution qt

Answer 1

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:

`\begin{cases}0.2x+0.8y={(0.4)(15)} \\ x+y=15\end{cases}`
`\begin{cases}0.2x+0.8y={6} \\ x+y=15\end{cases}`

In order to solve the exercise, you can use the Substitution Method:

1. Solve the second equation for "y":

`y=15-x`

2. Substitute the new equation into the first equation and solve for "x":

`0.2x+0.8(15-x)=6`
`0.2x+12-0.8x=6`
`\begin{gathered} x=(-6)/(-0.6) \\ \\ x=10 \end{gathered}`

3. Substitute the value into the second original equation and solve for "y":

`\begin{gathered} 10+y=15 \\ y=15-10 \\ y=5 \end{gathered}`

Hence, the answer is:

• 20% salt solution:

`10\text{ }qt`

• 80% salt solution:

`5\text{ }qt`