Gabe amodeo, a nuclear physicist needs 60 liters of a 40% acid solution. he currently has a 20% solution and a 50% solution. how many liters of each class does he need to make the needed 60 liters of 40% acid solution?

The correct answer is:

He needs 20 liters of the 20% solution and 40 liters of the 50% solution.

Explanation:

Let x represent the amount of the 20% solution and y represent the amount of the 50% solution.

The total amount of acid in the 20% solution would then be 0.2x; the total amount of acid in the 50% solution would be 0.5y.

We know that together, these make 60 liters of a 40% solution; this gives us the equation

0.2x+0.5y = 0.4(60)

Simplifying, we get

0.2x+0.5y = 2.4

We also know that the amounts of the 20% solution and 50% solution together give us 60 liters; this gives us the equation

x+y = 60

We now have a system of equations:

We will use elimination to solve this.  First we will make the coefficients of y equal; to do this, we will multiply the top equation by 2:

We will now cancel the y variables by subtracting the bottom equation:

Divide both sides by -0.6:

Substituting this into the second equation, we have

x+y = 60

20+y = 60

Subtract 20 from each side:

20+y-20 = 60-20

y = 40

sas (side angle side)

aa (angle angle)

sss(side side side)

sas find two sides with an angle in between

aa is finding two angles and the third will add up to 180

sss find all sides

step-by-step explanation: