a chemist has 200 ml of a 10% sucrose solution. she adds x ml of a 40% sucrose solution. the percent…

a chemist has 200 ml of a 10% sucrose solution. she adds x ml of a 40% sucrose solution. the percent concentration, y, of the final mixture is given by the rational function: y = (0.1(200)+0.4x)/(200 + x)·100. the chemist needs the concentration of the final mixture to be 30%. how many milliliters of the 40% solution should she add to the 10% solution to get this concentration? what is the total volume of the final mixture? what is the mass of sucrose in the final mixture?

a chemist has 200 ml of a 10% sucrose solution. she adds x ml of a 40% sucrose solution. the percent concentration, y, of the final mixture is given by the rational function: y = (0.1(200)+0.4x)/(200 + x)·100. the chemist needs the concentration of the final mixture to be 30%. how many milliliters of the 40% solution should she add to the 10% solution to get this concentration? what is the total volume of the final mixture? what is the mass of sucrose in the final mixture?

Answer

Answer:

180

Explanation:

Step1: Find the total volume of the final mixture

The chemist starts with 200 mL and adds 400 mL (as found from the previous - part of the problem where we determined the amount of 40% solution to add). So the total volume is (200 + 400=600) mL.

Step2: Calculate the mass of sucrose in the final mixture

The concentration of the final mixture is 30%. The total volume of the final mixture is 600 mL. The mass - volume percentage formula is (\text{mass}=\text{concentration}\times\text{volume}). The concentration (y = 30%=0.3) and the volume (V = 600) mL. So the mass of sucrose (m=0.3\times600 = 180) g.