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!

r and t.

both are 64 degrees.

delaney would like to make a 5lb nut mixture that is 60% peanuts and 40% almonds.

she has several pounds of peanuts and several pounds of a mixture that is 20% peanuts and 80% almonds.

let 'p' represent the number of pounds of peanuts needed to make the new mixture, and  

let 'm' represent the number of pounds of the 80% almond-20% peanut mixture.

:

p + m = 5

therefore

m = (5-p)

write an equation based on the percent of peanuts

1p + .2m = .6(5)

replace m with (5-p)

p + .2(5-p) = .6(5)

p + 1 - .2p = 3

p - .2p = 3 - 1

.8p = 2

p = 2/.8

p = 2.5 lbs of peanuts required

then

5 - 2.5 = 2.5 lbs of the peanut/almond mixture required

:

a) what is the system that models this situation?

p + m = 5

1p + .2m = .6(5)