a chemist currently has a solution of 30% hydrochloric acid and a solution of 15% hydrochloric acid. he…

a chemist currently has a solution of 30% hydrochloric acid and a solution of 15% hydrochloric acid. he mixes the two solutions together to create 24 ounces of a 25% hydrochloric acid solution. how many ounces of the 30% hydrochloric acid solution did he use in order to obtain the 25% solution?\n\na. 8 ounces\nb. 16 ounces\nc. 20 ounces\nd. 6 ounces

a chemist currently has a solution of 30% hydrochloric acid and a solution of 15% hydrochloric acid. he mixes the two solutions together to create 24 ounces of a 25% hydrochloric acid solution. how many ounces of the 30% hydrochloric acid solution did he use in order to obtain the 25% solution?\n\na. 8 ounces\nb. 16 ounces\nc. 20 ounces\nd. 6 ounces

Answer

Explanation:

Step1: Let the amount of 30% solution be $x$ ounces.

Let the amount of 15% solution be $y$ ounces. We know $x + y=24$ (total volume), so $y = 24 - x$.

Step2: Set up an equation based on acid - content.

The amount of acid in the 30% solution is $0.3x$, the amount of acid in the 15% solution is $0.15y$, and the amount of acid in the 25% solution of 24 ounces is $0.25\times24 = 6$. Substitute $y = 24 - x$ into the acid - content equation: $0.3x+0.15(24 - x)=6$.

Step3: Expand and simplify the equation.

$0.3x+3.6−0.15x = 6$. Combine like terms: $(0.3x−0.15x)+3.6 = 6$, which gives $0.15x+3.6 = 6$.

Step4: Solve for $x$.

Subtract 3.6 from both sides: $0.15x=6 - 3.6=2.4$. Then divide both sides by 0.15: $x=\frac{2.4}{0.15}=16$.

Answer:

B. 16 ounces