5. hailey would like to make a 5 lb coffee mixture that is 60% sumatra coffee bean blend. she has several pounds of a mixture that is 20% sumatra beans and another mixture blend with 80% sumatra beans . let x represent the amount of the 20% blend and y represent the amount of the 80% blend to find out how many pounds of each mixture hailey will need. (a) what is the system that models this situation? (b) what is the solution to the system: show your work.

A. The sum of the amount of both solutions to make up the mixture is shown below,
     
     x + y = 5

where x is the 20% Sumatra beans solution and y is the 80% Sumatra bean solution. Next, the amount of Sumatra bean before and after mixing are shown below,
    
     0.20x + 0.80y = 5(0.60)

The system of linear equations are therefore,
       x + y = 5
      0.2x + 0.8y = 3

b.
     x =5 - y
   0.2(5 - y) + 0.8y = 3

The value of y from the equation is 3.33 lbs. This gives us the value of x equal to 1.67. Thus, the solution to the system is,

       (1.67, 3.33)