Question

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? 0.5 liters 30 liters

Explanation:

Step1: Set up equation for acid - content

Let $x$ be the volume of the 20% acidic solution added. The amount of acid in the 50% solution is $0.5\times40$ liters, the amount of acid in the 20% solution is $0.2x$ liters, and the total volume of the final mixture is $(40 + x)$ liters with 30% acid - content, so $0.5\times40+0.2x=0.3(40 + x)$.

Step2: Expand and simplify the equation

First, expand the right - hand side: $20+0.2x = 12+0.3x$.

Step3: Solve for $x$

Subtract $0.2x$ from both sides: $20=12 + 0.3x-0.2x$. Then $20=12 + 0.1x$. Subtract 12 from both sides: $0.1x=20 - 12=8$. Divide both sides by 0.1: $x = 80$ liters. (It seems there is an error in the provided options as the correct answer is 80 liters)

Answer:

None of the provided options are correct. The correct amount is 80 liters.