Question

A surgeon needs 9 liters of a 3% saline solution. She has a 1% solution and a 10% solution available. How many liters of the 1% solution and how many liters of the 10% solution should she mix to make the 3% solution?

Answer 1

Let x liters of 1 % solution be mixed with y liters of 10% solution to prepare 9 liters of 3% saline solution.

Then x+y = 9…(1)

and x*0.01+y*0.10 = 9*0.03 or, 0.01x+0.1y = 0.27 or, on multiplying both the sides by 100, x+10y = 27…(2).

Now, on subtracting the 1^st equation from the 2^nd equation, we get x+10y –(x+y) = 27-9 or, 9y = 18 so that y = 18/9 = 2. Then, on substituting y = 2 in the 1^st equation, we get x+2 = 9 so that x = 9-2 = 7.

Thus, 7 liters of 1 % solution should be mixed with 2 liters of 10% solution to prepare 9 liters of 3% saline solution.