Q23. - Algebra 1

Question

Deon has 12 milliliters of a 5% solution. He also has a solution that has a concentration of 30% How many milliliters of the 30% solution does Deon need to add to the 30% solution to obtain a 20% solution?

Step-by-Step Solution

Answer

We need to add 18 milliliters of 30% solution to 12 milliliters of 5% to make the resulting solution 20%.

Step 1. Data.

Given Deon has 12 milliliters of a 5% solution. He also has a solution that has a concentration of 30%

Step 2. Analyse the data.

Let the millilitres of 30% solution added be $x$.

So, the total concentration when we add 12 milliliters of a 5% solution and $x$ milliliters of a 30% solution is given by

$12\cdot \frac{5}{100}+x\cdot \frac{30}{100}=\frac{60+30x}{100}$

Step 3. Solution.

We need to make 20% concentration of resulting solution.

So, the equation is given by:

$\begin{array}{l}\frac{60+30x}{100}=\left(12+x\right)\frac{20}{100}\\ \Rightarrow 60+30x=\left(12+x\right)20\\ \Rightarrow 60+30x=240+20x\\ \Rightarrow 30x-20x=240-60\\ \Rightarrow 10x=180\\ \Rightarrow x=18\end{array}$

Therefore, we need to add 18 milliliters of 30% solution to 12 milliliters of 5% to make the resulting solution 20%.