SOLUTION: Mr. Key has 50 liters of a 70% ethyl alcohol solution. How many liters of pure ethyl alcohol must be added to obtain an 80% ethyl alcohol solution? How many liters of each soluti

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Mr. Key has 50 liters of a 70% ethyl alcohol solution. How many liters of pure ethyl alcohol must be added to obtain an 80% ethyl alcohol solution? How many liters of each soluti      Log On


   

Question 169045: Mr. Key has 50 liters of a 70% ethyl alcohol solution. How many liters of pure ethyl alcohol must be added to obtain an 80% ethyl alcohol solution? How many liters of each solution did he have? I am stumped. Please explain how I put into a chart and how I can get the answer. I appreciate your help.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = the number of liters of pure (100%) ethyl alcohol to be added to the 50 liters of 70% ethyl alcohol solution to obtain 50+x liters of 80% ethyl alcohol solution.
Change the percentages to their decimal equivalents:
70% = 0.7
80% = 0.8
Now you can write the equation to sove for x:
50(0.7)+x = (50+x)(0.8) Simplify.
35+x = 40+0.8x Subtract 0.8x from both sides.
35+0.2x = 40 Subtract 35 from both sides.
0.2x = 5 Divide both sides by 0.2
x = 25
Mr. Key will need to add 25 liters of pure (100%) ethyl alcohol to the 50 liters of 70% alcohol solution to obtain 75 liters of 80% alcohol solution.