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A scientist needs to make 5.4 liters of saline solution (salt water), in which the salt level must be at 28% concentration (meaning 28% of the water is salt). Unfortunately, the scientist only has two types of saline solution in his possession. He has saline solution with a 12% concentration level and saline solution with a 30% concentration level.

How much of each type of saline solution should the scientist mix together to achieve 5.4 liters of saline solution at a concentration level of 28%?

Sagot :

Facundo3141592idn

By solving a system of equations, we will see that the scientist needs to use:

  • 1.444 liters of the 12% solution.
  • 3.956 liters of the 30% solution.

How to find the system of equations?

First, we need to define the variables, we will use:

  • x = liters of the 12% solution used.
  • y = liters of the 30% solution used.

We know that the scientist needs 5.4 liters, then we will have that:

x + y = 5.4

We also know that the end concentration for these 5.4 liters must be 28%, then the concentration in the left side must be the same as the one in the right side, this gives the equation:

0.12*x + 0.30*y = 0.28*(5.4)

0.12*x + 0.30*y = 1.512

Then the system of equations is:

x + y = 5.4

0.12*x + 0.30*y = 1.512

To solve it, we first need to isolate one of the variables in one of the equations, I will isolate x in the first one.

x = 5.4 - y

Now we can replace this in the other equation to get:

0.12*(5.4 - y) + 0.30*y = 1.512

0.81 - 0.12*y + 0.30*y = 1.512

(0.30 - 0.12)*y = 1.512 - 0.81

0.18*y = 0.712

y = (0.712)/0.18 = 3.956

And to find the value of x, we use:

x = 5.4 - y = 5.4 - 3.956 = 1.444

So the scientist needs to use:

  • 1.444 liters of the 12% solution.
  • 3.956 liters of the 30% solution.

If you want to learn more about systems of equations, you can read:

https://brainly.com/question/13729904

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