5 home work

Question

How many gallons of 25 % alcohol solution and 50 % alcohol solution must be mixed to get 20 gallons of 40 % alcohol solution?

There needs to be gallons of 25% alcohol solution and gallons of 50% solution.

Answer 1

If x= gallons of 25% alcohol solution then alcohol is .25x

If y = gallons of 50% alcohol solution then alcohol is .5y

 

x+y = 40

y = 40-x

 

Gallons of alcohol in final solution is .4(x+y) = .4(40) = 16

 

.25x + .5y = 16

.25x + .5(40-x) = 16

.25x + 20 - .5x = 16

-.25x = -4

x = -4/(-.25)

x = 16

 

y=40-x = 24

 

16 gallons of 25% solution and 24 gallons of 50% solution