Q 4.53 - Intermediate Algebra

Question

Translate to a system of equations and solve:

LeBron needs $150$ millilitres of a $30\%$ solution of sulfuric acid for a lab experiment but only has access to a $25\%$ and a $50\%$ solution. How much of the $25\%$ and how much of the $50\%$ solution should he mix to make the $30\%$ solution?

Step-by-Step Solution

Answer

The volume of $25\%$ of solution mixed  is $120 ml$

The volume of $50\%$ of solution mixed is $30 ml$

Step 1 . Given Information

• The volume of solution needed is $150 ml$ of $30\%$ of sulphuric acid.
• The concentration we have is $25\%$ and $50\%$ of sulphuric acid.

Step 2. Form the equations

Let

$$\begin{gathered} x = number of ml of 25\% solution. \\ y = number of ml of 50\% solution \end{gathered}$$

So, according to the question,

$x+y=150\_\_\_\left(1\right)$

The total volume of sulphuric acid at $30\%$ is:

$$\begin{gathered} =150\times 30\% \\ =150\times 0.30 \\ =45 ml \end{gathered}$$

So, according to question,

$0.25x+0.50y=45\_\_\_\left(2\right)$

Step 3. Solve the system of equations by the elimination method.

Multiplying equation $\left(1\right)$ by $0.25$, we get:

$$\begin{gathered} 0.25(x+y)=0.25\times 150 \\ 0.25x+0.25y=37.5\_\_\_\_\left(3\right) \end{gathered}$$

Subtracting equation $\left(3\right)$ from equation$\left(2\right)$, we get:
$$\begin{gathered} (0.25x+0.50y)-(0.25x+0.25y)=45-37.5 \\ 0.25y=7.5 \end{gathered}$$

Dividing both sides by $0.25$ , we get:

$$\begin{gathered} \frac{0.25y}{0.25}=\frac{7.5}{0.25} \\ y=30 \end{gathered}$$

Step 4. Find the value of x

Substituting the value $y=30$ in the equation $\left(1\right)$, we get:

$$\begin{gathered} x+y=150 \\ x+30=150 \\ x+30-30=150-30 \\ x=120 \end{gathered}$$

So, LeBron should mix $120 ml$ of $25\%$ solution and $30 ml$ of $50\%$ solution