Question

Can you explain step by step for #15 and #16 I have a test on this tomorrow

Answer 1

Answer:

15.

$\left\{\begin{array}{l}x+y=50\\0.2x+0.1y=6\end{array}\right.$

16. 10 ml of 20% saline and 40 ml of 10% saline

Step-by-step explanation:

A chemist takes x ml of 20% saline and y ml of 10% saline. In total, he takes

x + y ml that is 50 ml, so

$x + y = 50.$

There are  $0.2x$ ml of salt in x ml of 20% saline and $0.1y$ ml of salt in 10% saline. There are $0.12\cdot 50=6$ ml of salt in 50 ml of 12% saline. Thus,

$0.2x+0.1y=6$

15. We get the system of two equations:

$\left\{\begin{array}{l}x+y=50\\0.2x+0.1y=6\end{array}\right.$

16. Solve this system. From the first equation:

$x=50-y$

Substitute it into the second equation:

$0.2(50-y)+0.1y=6\\ \\10-0.2y+0.1y=6\\ \\-0.1y=6-10\\ \\-0.1y=-4\\ \\y=40\\ \\x=50-y=50-40=10$