Question

9. A chemistry teachers needs 25 liters of a 12% salt solution. The teacher has mixture of a 5%

salt solution and a mixture of a 20%, salt solution. How many liters of the 5% and 20% mixture
should she mix to get what she needs? Round your answer to the nearest tenth if necessary. Be
sure to write down your equation (equation: 2 pts, solution: 2 points, answer: 1 pt)

Answer 1

13.3 L of 5% salt solution and 11.7 L of 20% salt solution

Explanation:

Let

x L = amount of 5% solution

y L = amount of 20% solution.

1. A chemistry teachers needs 25 liters of salt solution, then

`x+y=25`

2. A chemistry teachers needs 25 liters of a 12% salt solution, so there are

`25\cdot 0.12=3` liters of salt.

Amount of salt in 5% solution
`=x\cdot 0.05=0.05x` liters

Amount of salt in 20% solution
`=y\cdot 0.2=0.2y` liters,

thus

`0.05x+0.2y=3`

3. Solve the system of two equations:

`\left\{\begin{array}{l}x+y=25\\ \\0.05x+0.2y=3\end{array}\right.`

From the first equation,

`x=25-y`

Substitute it into the second equation:

`0.05(25-y)+0.2y=3\\ \\1.25-0.05y+0.2y=3\\ \\0.2y-0.05y=3-1.25\\ \\0.15y=1.75\\ \\15y=175\\ \\y\approx 11.7\ L\\ \\x=25-11.7=13.3\ L`