Question

Translate to a system of equations and solve:

LeBron needs 150 milliliters 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?

Short answer

The number of units of 25% solution and number of units of 50% solution are 120 and 30 respectively.

Step-by-step solution

Step 1. Given Information  

The given data is that LeBron needs 150 milliliters of a 30% solution of sulfuric acid for a lab experiment but only has access to a 25% and a 50% solution.

Step 2. Explanation 

Let number of units of 25% solution be x and number of units of 50% solution be y.

The number of units of 30% solution required is 150 ml.

Thus, total units of solution is $x+y=150--\left(1\right)$

The amount of 30% solution is $150\times 0.3=45$

And total amount of solution can be expressed asrole="math" localid="1647681028264" $0.25x+0.5y=45--\left(2\right)$

Step 3. Calculation

Multiply equation (1) with $0.5$and write the revised equation.

$$\begin{gathered} 0.5(x+y)=0.5\left(150\right) \\ 0.5x+0.5y=75--\left(3\right) \end{gathered}$$

Solve the equations (2) and (3) by subtracting equation (2) from equation (3) to find the value of x.

$$\begin{gathered} 0.5x+0.5y-0.25x-0.5y=75-45 \\ 0.25x=30 \\ x=120 \end{gathered}$$

Substitute the value of x in equation (1) to find the value of y.

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