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

expression #3 is not equivalent. the others are.