90.3k views
1 vote
In the lab, Deandre has two solutions that contain alcohol and is mixing them with each other. Solution A is 10% alcohol and Solution B is 60% alcohol. He uses200 milliliters of Solution A. How many milliliters of Solution B does he use, if the resulting mixture is a 40% alcohol solution?

User Edl
by
7.9k points

1 Answer

1 vote

The percentage of alcohol of a solution i is given by the quotient:


p_i=(v_i)/(V_i),_{}

where v_i is the volume of alcohol in the solution i and V_i is the volume of the solution i.

From the statement of the problem we know that:

1) Solution A has 10% of alcohol, i.e.


p_A=\frac{v_A_{}}{V_A}=0.1.\Rightarrow v_A=0.1\cdot V_A.

2) Solution B has 60% of alcohol, i.e.


p_B=(v_B)/(V_B)=0.6\Rightarrow v_B=0.6\cdot V_B.

3) The volume of solution A is V_A = 200ml.

4) The resulting mixture must have a percentage of 40% of alcohol, so we have that:


p_M=(v_M)/(V_M)=0.4.

5) The volume of the mixture v_M is equal to the sum of the volumes of alcohol in each solution:


v_M=v_A+v_{B\text{.}}_{}

6) The volume of the mixtureVv_M is equal to the sum of the volumes of each solution:


V_M=V_A+V_B\text{.}

7) Replacing 5) and 6) in 4) we have:


\frac{v_A+v_B}{V_A+V_B_{}}=0.4_{}\text{.}

8) Replacing 1) and 2) in 7) we have:


(0.1\cdot V_B+0.6\cdot V_B)/(V_A+V_B)=0.4_{}\text{.}

9) Replacing 3) in 8) we have:


\frac{0.1\cdot200ml_{}+0.6\cdot V_B}{200ml_{}+V_B}=0.4_{}\text{.}

Now we solve the last equation for V_B:


\begin{gathered} \frac{0.1\cdot200ml+0.6\cdot V_B}{200ml_{}+V_B}=0.4_{}, \\ \frac{20ml+0.6\cdot V_B}{200ml_{}+V_B}=0.4_{}, \\ 20ml+0.6\cdot V_B=0.4_{}\cdot(200ml+V_B), \\ 20ml+0.6\cdot V_B=80ml+0.4\cdot V_B, \\ 0.6\cdot V_B-0.4\cdot V_B=80ml-20ml, \\ 0.2\cdot V_B=60ml, \\ V_B=(60)/(0.2)\cdot ml=300ml. \end{gathered}

We must use 300ml of Solution B to have a 40% alcohol solution as the resulting mixture.

Answer: 300ml of Solution B.

User Miluska
by
8.5k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories