Ascientist needs 70 liters of a 40% solution of alcohol. he has a 30% and a 60% solution available. how many liters of the 30% and how many liters of the 60% solutions should he mix to make the 40% solution?

The answer is:

There are needed 46.67 liters of the 30% solution and 23.33 liters of the 60% solution in order to make 70 liters of a 40% solution.

We can solve this problem creating a system of equations. Let's make the two equations that will help us to solve the problem.

From the statement we know that a solution of 70 liters of a 40% is needed, and there are two differents solutions available, of 30% and 60% and we need to use them to make 70 liters of a  40% solution, so:

So:

If both solutions will make a 70 liters solution, so the first equation will be:

Let's work with real numbers converting the percent values into real numbers by dividing it into 100, so:

Then, we know that both solutions will make 70 liters of a 40% solution, so the second equation will be:

Therefore, from the first equation we have:

Then, substituting x into the second equation to find y, we have:

Hence, substituting y into the first equation to find x, we have:

So, there are needed 46.67 liters of the 30% solution and 23.33 liters of the 60% solution in order to make 70 liters of a 40% solution.

Have a nice day!

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!