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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)

Respuesta :

frika

Answer:

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

Step-by-step 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

[tex]x+y=25[/tex]

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

[tex]25\cdot 0.12=3[/tex] liters of salt.

Amount of salt in 5% solution [tex]=x\cdot 0.05=0.05x[/tex] liters

Amount of salt in 20% solution [tex]=y\cdot 0.2=0.2y[/tex] liters,

thus

[tex]0.05x+0.2y=3[/tex]

3. Solve the system of two equations:

[tex]\left\{\begin{array}{l}x+y=25\\ \\0.05x+0.2y=3\end{array}\right.[/tex]

From the first equation,

[tex]x=25-y[/tex]

Substitute it into the second equation:

[tex]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[/tex]

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