please help!!!!!!!

Question

1.) A mixture of 4% disinfectant solution is to be made from 6% and 3% disinfectant solutions. How much of each solution should be used if 27 gallons of 4% solution are needed?

2.) How many liters of 80% alcohol solution and 40% alcohol solution must be mixed to obtain 4 liters of 50% alcohol solution?

3.) For a Saturday matinee, adult TICKETS cost $5.50 and kids under 12 pay only $3.00. If 50 TICKETS are sold for a total of $200, how many of the tickets were adult tickets and how many were sold to kids under 12?

4.)How many liters of 80% alcohol solution and 30% alcohol solution must be mixed to obtain 15 liters of 60% alcohol solution? 

Answer 1

x = volume of 6% solution 

y = volume of 3% solution 

 

The total volume of 4% solution is 27. We construct one equation for total volume & another for total disinfectant.

 

Volume: x+y = 27

Disinfectant: .06x + .03y = 27*.04 = 1.08

 

System of equations:

x+y = 27

.06x + .03y = 1.08

 

Divide second equation by .06:

 

x+y = 27

x+.5y = 18

 

Subtract the two equations:

 

.5y = 9

y = 18 gallons

x = 9 gallons

 

We need 9 gallons of the 6% solution & 18 gallons of the 3% solution to get 27 gallons of a 4% solution.