a scientist has 40 liters of a 50% acidic solution. she adds a 20% acidic solution to create a mixture that…

a scientist has 40 liters of a 50% acidic solution. she adds a 20% acidic solution to create a mixture that has been diluted to have 30% acidity. the graph models the percent of acidity in the final mixture. how many liters of the 20% acidic solution should be added to create the needed 30% acidity in the final mixture?

a scientist has 40 liters of a 50% acidic solution. she adds a 20% acidic solution to create a mixture that has been diluted to have 30% acidity. the graph models the percent of acidity in the final mixture. how many liters of the 20% acidic solution should be added to create the needed 30% acidity in the final mixture?

Answer

Explanation:

Step1: Set up the equation

Let $x$ be the volume of the 20% acidic solution. The amount of acid in the 50% solution is $0.5\times40$, the amount of acid in the 20% solution is $0.2x$, and the total volume of the final - mixture is $40 + x$ with an acid - content of $0.3(40 + x)$. So the equation is $0.5\times40+0.2x=0.3(40 + x)$.

Step2: Expand and simplify the equation

First, expand the right - hand side: $0.5\times40+0.2x=0.3\times40+0.3x$. Then, calculate $0.5\times40 = 20$ and $0.3\times40 = 12$. The equation becomes $20+0.2x=12 + 0.3x$.

Step3: Solve for $x$

Subtract $0.2x$ from both sides: $20=12 + 0.3x-0.2x$. Simplify to get $20=12 + 0.1x$. Then subtract 12 from both sides: $20 - 12=0.1x$. So $8 = 0.1x$. Divide both sides by 0.1: $x=\frac{8}{0.1}=80$.

Answer:

80