Question

bruce wants to make 50 ml of an alcohol solution with a 12% concentration. he has a 10% alcohol solution and a 15% alcohol solution. the equation $0.10x + 0.15(50 - x) = 0.12(50)$ can be used to find the amount of 10% alcohol solution bruce should use.

how much of the 10% alcohol solution should bruce use?

\boxed{} ml

how much of the 15% alcohol solution should bruce use?

\boxed{} ml

Explanation:

Step1: Simplify the equation

We start with the equation \(0.10x + 0.15(50 - x)=0.12(50)\). First, expand the terms: \(0.10x + 7.5- 0.15x = 6\).

Step2: Combine like terms

Combine the \(x\) terms: \(0.10x-0.15x=- 0.05x\). So the equation becomes \(-0.05x + 7.5=6\).

Step3: Solve for \(x\)

Subtract 7.5 from both sides: \(-0.05x=6 - 7.5=-1.5\). Then divide both sides by \(- 0.05\): \(x=\frac{- 1.5}{-0.05}=30\).

Step4: Find the amount of 15% solution

The amount of 15% solution is \(50 - x\). Since \(x = 30\), then \(50-30 = 20\).

Answer:

For the 10% alcohol solution: 30 ml
For the 15% alcohol solution: 20 ml