Algebra formula

Question

James Callahan 10% alcohol solution and a 60% alcohol solution. Find how many liters of each solution he should mix to make 50 liters of a 40% alcohol solution. How many liters of 60% alcohol solution must be used in the mixture?

Answer 1

Let

x-------------> liters of 10% alcohol solution

y-------------> liters of 60% alcohol solution

we know that

x+y=50----------------------> x=50-y-----------------> equation 1

0.10x+0.60y=0.40*50----------> 0.10x+0.60y=20---------> equation 2

substitute 1 in 2 

0.10*(50-y)+0.60y=20---------> 5-0.10y+0.60y=20

5+0.50y=20------------> 0.50y=15-----------------> y=30

x+y=50----------> x=50-30---------> x=20

the answer is

20 liters of 10% alcohol solution

30 liters of 60% alcohol solution