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. which equation can bruce use to determine how much of the 10% alcohol solution he should use? (0.10x)(0.15)(50 - x) = 0.12(50) 0.10x + 0.15(50 - x) = 50 + 0.12 0.10x + 0.15(50 - x) = 50 + 0.12 + 0.12(50) 0.10x + 0.15(50 - x) = 0.12(50)

Explanation:

Step1: Define Variables

Let \( x \) be the volume (in ml) of the 10% alcohol solution. Then the volume of the 15% alcohol solution is \( 50 - x \) ml (since the total volume is 50 ml).

Step2: Calculate Alcohol Amounts

• The amount of alcohol in the 10% solution is \( 0.10x \) (because 10% of \( x \) ml is alcohol, so \( 0.10 \times x \)).
• The amount of alcohol in the 15% solution is \( 0.15(50 - x) \) (15% of \( 50 - x \) ml is alcohol).
• The amount of alcohol in the final 50 ml solution (with 12% concentration) is \( 0.12 \times 50 \).

Step3: Set Up the Equation

The total amount of alcohol from the two solutions should equal the amount of alcohol in the final solution. So we set up the equation:
\( 0.10x + 0.15(50 - x) = 0.12(50) \)

Answer:

\( 0.10x + 0.15(50 - x) = 0.12(50) \) (the fourth equation)