Question

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 combine to create the 30% solution?

Answer 1

Answer:

She should add 72 ml of the 20%-acidic solution and 48 ml of the 45%-acidic solution.

Step-by-step explanation:

Hi there!

The volume of the final solution will be the sum of the volume of each solution:

let x be the volume of the solution that is 20% acidic and y the volume of the solution that is 45% acidic. Then:

x + y = 120 ml

The amount of acid (let´s call it acidity units) of the total solution will be the sum of the amount of acid of each solution. If the final solution has 30 acidity units in 100 ml, then in 120 ml there will be (120 ml · 30 acidity units / 100 ml) 36 acidity units (concentration times volume over 100). Then the sum of the acidity units can be expressed as follows:

20/100 x + 45/100 y = 36

0.2x + 0.45y = 36

Then, we have a system of equations that we can solve because there are two equations and two unknowns:

x + y = 120 ml

0.2x + 0.45 y = 36

The solution of the system will be the pair (x,y) that satisfies both equations.

Let´s take the first equation and solve it for y:

x + y = 120 ml

subtract x to both sides of the equation

y = 120 - x

Now replace y in the second equation:

0.2x + 0.45 y = 36

0.2x + 0.45(120 - x) = 36

Apply distributive property

0.2x + 54 - 0.45x = 36

subtract 54 to both sides of the equation

-0.25x = 36 - 54

-0.25x = -18

divide both sides of the equation by -0.25

x = -18/-0.25

x = 72

Now, let´s calculate y:

y = 120 - x

y = 120 - 72

y = 48

She should add 72 ml of the 20%-acidic solution and 48 ml of the 45%-acidic solution.