a biologist has three salt solutions: some 5% solution, some 15% solution, and some 25% solution. She needs to mix some of each to get 50 liters of 20% solution. She wants to use twice as much of the 5% solution as the 15% solution. How much of each solution should she use?

Question

I've been trying to figure out the equation but I'm so stumped :(

Answer 1

If the amounts of 5%,15% and 25% are x,y,z then we have

x+y+z = 50
.05x + .15y + .25z = .20(50)
x = 2y

Replace x with 2y and you have

2y+y+z = 50
.05(2y) + .15y + .25z = .20(50)
or,
3y+z = 50
.25y + .25z = 10

3y+z = 50
y+z = 40
So, subtracting, we get
2y=10
y=5
so, x=2y=10
10+5+z=50, so z=35