SOLUTION: confused on this word problem..need helpppp 20% alcohol solution and 70% alcohol solution available. how many liters of each must the pharmacy use to make a mixture containing 5

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Question 994279: confused on this word problem..need helpppp
20% alcohol solution and 70% alcohol solution available. how many liters of each must the pharmacy use to make a mixture containing 50 liters of 60% alcohol solution?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
x= liters of 20% alcohol solution to be used
y= liters of 70% alcohol solution to be used
0.2x= liters of alcohol in x liters of 20% alcohol solution
0.7y= liters of alcohol in y liters of 70% alcohol solution
0.6%2A50=30= liters of alcohol in 50 liters of 60% alcohol solution
When you mix the two solutions you want:
a total volume of 50 liters, so x%2By=50 , and
a total alcohol amount of 30 liters, so 0.2x%2B0.7y=30 .
So you have to solve
system%28x%2By=50%2C0.2x%2B0.7y=30%29 .

Solving:
system%28x%2By=50%2C0.2x%2B0.7y=30%29-->system%28y=50-x%2C0.2x%2B0.7y=30%29-->
system%28y=50-x%2C0.2x%2B0.7%2850-x%29=30%29-->system%28y=50-x%2C0.2x%2B0.7%2A50-0.7x=30%29-->
system%28y=50-x%2C0.2x%2B35-0.7x=30%29-->system%28y=50-x%2C0.2x%2B35-0.7x=30%29-->system%28y=50-x%2C35-0.5x=30%29-->
system%28y=50-x%2C35-30=0.5x%29-->system%28y=50-x%2C5=0.5x%29-->
system%28y=50-x%2Cx=10%29-->system%28y=50-10%2Cx=10%29-->highlight%28system%28y=40%2Cx=10%29%29
The pharmacy should mix 10 liters of 20% alcohol solution and 40 liters of 70% alcohol solution.

NOTE:If you did not study systems of equations, then use 50-x instead of y , first find x from 0.2x%2B0.7%2850-x%29=30 ;
0.2x%2B0.7%2850-x%29=30-->0.2x%2B0.7%2A50-0.7x=30-->0.2x%2B35-0.7x=30-->
35-0.5x=30-->-0.5x=30-35-->-0.5x=-5-->x=%28-5%29%2F%28-0.5%29-->highlight%28x=10%29 .
Then you calculate 50-x=highlight%2840%29