Achemist has one solution that is 60% alcohol and another that is 35% alcohol. how much of each must she use to make 15 liters of a solution is 50% alcohol?

Let x represent the total amount litters of solutions for 60% alcohol
15-x represent the total amount of litters of solutions for 35% alcohol, so:
0.6(x)+0.35(15-x)=0.5(15)
0.6x+5.25-0.35x=7.5
0.25x+5.25=7.5
Subtract 5.25 to each side
0.25x+5.25-5.25=7.5-5.25
0.25x=2.25
Divided 0.25 to each side
0.25x/0.25=2.25/0.25
x=9 liters
15-x
=15-9
=6 litters. As a result, she must use 9 litters of 60% alcohol and 6 litters of 35% alcohol to make 50% alcohol. Hope it help!