A scientist wants to create 120 ml of a solution that is 30% acidic. To create this solution, she has access to a 20% solution and a 45% solution. How many milliliters of each solution should she

Question

combine to create the 30% solution?

Should this be solved using three variables?

Answer 1

Let x = amount of 20% solution

120-x = amount of 45% solution

Then,

{ 20x + 45(120-x) }/(x+120-x) = 30

Solving for x:

25x = 1800

x = 72 ml of 20% solution

120-x = 48 ml of 45% solution

Answer 2

This can be solved using a system of two equations and two variables.

Let x = amount of mL the 20% acid solution

Let y = amount in mL of the 45% acid solution

We know the total mL's of the mixture of the two solutions is 120 mL,,, so x + y = 120

20% of solution x is acid which can be written as .20 x and similarly acid from second solution can be written as .45 y. We know that 30% of the 120 mL solution will be acid or ..30 (120).

The acid in mixture solution comes from the acid in solution x and solution y. So .20 x + .45 y = .30 (120)

We now have system of equations to solve

x + y = 120

20 x + .45 y = .30 (120)

From here solve the system using substitution or elimination.