Algebra homework help

Question

An iodine solution is essentially a mixture of water and the element iodine. An iodine solution is described using a percentage which indicates what percent of the entire solution is iodine only. 

Information:

You have one beaker which contains an unknown amount of a 15% iodine solution and another beaker which contains an unknown amount of a 20% iodine solution. You also have a third beaker which contains 100 mL of a 10% solution.  

You add only half of the 20% solution to the 15% solution, and the mixture becomes an 18% solution. Then you add 50 mL of the 10% solution to the whole mixture. After this, the whole entire mixture of the 15% solution, half of the 20% solution, and 50mL of a 10% solution becomes a 14% solution.

How much liquid (in mL) was originally in the beaker with the 20% solution and how much liquid (in mL) was originally in the beaker with the 15% solution?

Answer 1

Steps:

1) Label data in color (be sure to keep it straight!)

2) Setup a chart to organize the data

3) Take each amount, multiply by the percentage as a decimal for each mixtures.

4) The mixtures are the multiplication of the percentages, but also equal to the sum of the two components mixed into the mixture.

5) You end up with 2 equations & 2 unknowns, whichi is a linear system. You have several options to solve.

6) We solve by substitution., 3x = y

7) We find x = 20 mL, y = 60 mL

8) We confirm using graphing intersection of lines that this is the correct answer.