A 12% brine solution was mixed with a 16% brine solution to produce a 15% brine solution. How much of the 12% solution and how much of the 16% solution were used to produce 40 L of the 15% solution?

Answer:

10 liters

Step-by-step explanation:

x=12% solution, y=16% solution

x+y=40

0.12x+0.16y=6 .   (12x+16x=600)

-12x-12y=-480

      12x+16x=600

+     -12x-12y=-480

-------------------------------

             4x=120

x=30

12% solution= 30 liters

16% solution= 10 liters

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

10L of the 12% of solutions and 30L of the 16% of solutions were used to produce 40L of the 15% of solutions.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

Let 12% brine solution be x.

Let 16% brine solutions be y.

12% brine solution was mixed with a 16% brine solution to produce 40L of the 15% solution.

This can be written as,

x + y = 40 ______(1)

0.12x + 0.16y = 0.15 x 40

0.12x + 0.16y = 6 _______(2)

We will solve for x and y.

From (1) we get,

x + y = 40

x = 40 - y _____(3)

Putting ( 3) in (2)

0.12 (40 - y) + 0.16y = 6

4.8 - 0.12y + 0.16y = 6

4.8 + 0.04y = 6

0.04y = 6 - 4.8

0.04y = 1.2

y = 1.2/0.04

y = 30

Putting in (3) we get,

x = 40 - 30 = 10

Thus,

10L of the 12% of solutions and 30L of the 16% of solutions were used to produce 40L of the 15% of solutions.

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