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? 0.5 liters 30 liters
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 a 30% acid concentration. So the equation is $0.5\times40+0.2x=0.3(40 + x)$.
Step2: Expand the equation
$20+0.2x = 12+0.3x$.
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: $x = 80$.