In a laboratory a pharmacist has 30% and 80% alcohol solutions. she needs 100ml of a 50% alcohol solution. how many milliliters of the 30% and 80% solutions should she mix?

this is from a homework i dont really understand would you mind showing your work

Let:
x=ml of 30% alcohol solution
y=ml of 80% alcohol solution.

100 ml of  50% alcohol  solution has 50 ml of alcohol and 50 ml of water.
50 % of 100 ml=(50/100)100 ml=50 ml

ml of alcohol in a 30% alcohol solution=0.3 (number of ml of 30% alcohol solution). In this case would be: 03x
 
ml of alcohol in a 80% alcohol solution=0.3 (number of ml of 30% alcohol solution). In this case would be: 0.8y

We can suggest this system of equations:
x+y=100
0.3x+0.8y=50

We can solve this system of equations by substitution method:
x+y=100 ⇒     y=100-x

0.3x+0.8(100-x)=50
0.3x+80-0.5x=50
 0.3x-0.5x=50-80
-0.2x=-30
x=-30/(-0.2)
x=60

y=100-x
y=100-60
y=40

She should mix 60 ml of a 30% alcohol soluiton with 40 ml of 80% alcohol solution.

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