A scientist needs 90 liters of a 50% acid solution. He currently has a 30% solution and a 60% solution. How many liters of each does he need to make 90 liters of 50% acid solution?

Answer 1

You need two equations: one for solution amounts and one for alcohol amounts. Here they are

90 = X + Y

45 = (0.6)/X + (0.3)Y

Here X = amount of 60 % solution and Y = amount of 30 percent solution. Note that percentages have been converted to decimal amounts in the second equation.

From here you have to solve two equations with two unknowns. Easiest to solve first equation for X = 90 - Y, then substitute into second equation. this get you one equation in one unknown. Solving you you will get

X = 30 liters and Y = 60 liters.

Hope this helps you out.

Answer 2

X+Y = 90

0.3X + 0.6Y = 0.5*90 = 45

0.3(90 - y) + 0.6y = 45

27 - 0.3y + 0.6y = 45

27 + 0.3y = 45

0.3y = 18

3y = 180

y = 60

x = 30

30 liters of the 30%

60 liters of the 60%