Question

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

Answer 1

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

$x+y=25$

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:

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