A factory has a batch of hand sanitizer with 50% alcohol content. How much pure 100% concentration) alcohol should they include in a 600mL bottle to make a 68% mixture? mL

Question

A factory has a batch of hand sanitizer with  50% alcohol content. How much pure  100% concentration) alcohol should they include in a  600mL bottle to make a  68% mixture?  mL

Bytelearn · Accepted Answer

Denoting the amount of pure alcohol: Let's denote the amount of pure alcohol to be added as x mL. The current solution has 50% alcohol content, which means there are 600 mL * 50% = 300 mL of alcohol in the 600 mL bottle. We want to add x mL of pure alcohol to this to achieve a 68% alcohol mixture in the final solution.Calculating the total volume and alcohol content: The total volume of the new solution will be 600 mL + x mL. The total amount of alcohol in the new solution will be 300 mL (from the original solution) + x mL (from the pure alcohol added).Setting up the equation for alcohol concentration: We want the final solution to have a 68% alcohol concentration. Therefore, the equation representing the alcohol content of the final solution is: (300 mL + x mL) / (600 mL + x mL) = 68%Converting the percentage to a decimal: To solve for x, we first convert the percentage to a decimal by dividing by 100: (300 + x) / (600 + x) = 0.68Eliminating the denominator: Now we multiply both sides of the equation by (600 + x) to get rid of the denominator: (300 + x) = 0.68 * (600 + x)Distributing 0.68 on the right side: Distribute 0.68 on the right side of the equation: 300 + x = 0.68 * 600 + 0.68xSimplifying the equation: Simplify the equation by performing the multiplication: 300 + x = 408 + 0.68xCombining like terms: Subtract 0.68x from both sides to get all the x terms on one side: 300 + x - 0.68x = 408Isolating the x term: Combine like terms: 300 + 0.32x = 408Performing the subtraction: Subtract 300 from both sides to isolate the x term: 0.32x = 408 - 300Solving for x: Perform the subtraction: 0.32x = 108Finding the value of x: Divide both sides by 0.32 to solve for x: x = 108 / 0.32Perform the division to find the value of x: x = 337.5

A factory has a batch of hand sanitizer with $50 \%$ alcohol content. $\newline$ How much pure $(100 \%$ concentration) alcohol should they include in a $600 \mathrm{~mL}$ bottle to make a $68 \%$ mixture? $\newline$ $\mathrm{mL}$

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A factory has a batch of hand sanitizer with 50% 50 \% 50% alcohol content.\newlineHow much pure (100% (100 \% (100% concentration) alcohol should they include in a 600 mL 600 \mathrm{~mL} 600 mL bottle to make a 68% 68 \% 68% mixture?\newlinemL \mathrm{mL} mL

A factory has a batch of hand sanitizer with $50 \%$ alcohol content. $\newline$ How much pure $(100 \%$ concentration) alcohol should they include in a $600 \mathrm{~mL}$ bottle to make a $68 \%$ mixture? $\newline$ $\mathrm{mL}$