Ethan needs to produce 2000 milliliters of 65% alcohol solution At his disposal he has 80% solution and 60% alcohol solution How much of each does he need in order to produce his desired solution

Question

He needs ___ milliliters of 80% solution

He needs ___ milliliters of 60% solution

Answer 1

simplify by using units of 1000 ml

then 60x + 80(2-x) = 65(2)

-20x = 130-160

x = 30/20 = 1.5 = 1500 ml of 60% solution

and 500 ml of 80% solution to get 2000 ml of 65% solution.

Answer 2

let x ml 80% solution and (2000 - x) ml 60% solution.

We have equation: 0.80x + 0.60(2000 - x) = 0.65·2000;

0.80x + 1200 - 0.60x = 1300;

0.20x = 100; x = 500 ml; 2000 - 500 = 1500 ml

Answer 3

Okay so this question is a system of equations.

Let's start by defining our variables.

Let x= 60 percent solution in mL and y= 80 percent solution

So the question tells us the solution will be 2000 mL

x+y=2000

Now the question also tells us that the he wants a solution with a 65 percent solution

(.60x+.80y)/(2000)=.65

Multiply by 2000, we get

.60x+.80y=1300

Then will take our first equation and solve for x

x=2000-y

Will then substitute it in for are x value in equation 2

.60(2000-y)+.80y=1300

simplify,

1200-.60y+.80y=1300

Add like terms

.20y=100

divide by .20

y=500

substitute for 500 for y in our first equation

x+y=2000

x+(500)=2000

x=1500

Then we have x=500 and y=1500, which means that we have 1500 mL of the 60 percent solution and 500 0f the 80 percent mL solution.

Answer 4