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 th
at 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.
<span>Mixture is 5lb = x + y => y = 5 - x
From the given information 20% x + 80%y = 60% x 5
So 2x + 8(5 - x) = 6 x 5 => 40 - 6x = 30 => 10 = 6x => x = 5 / 3 => y = 5 - (5/3) => y = 10 / 3
20% Sumatra beans = 5 / 3
80% Sumatra beans = 10 / 3.
The system that models this situation is system of equations.</span>
A] Given that the number of the unknowns are two, that is, x which represents the amount of the 20% blend and y which represents the amount of 80% blend, the system that models this situation is simultaneous equation.
b] The solution to the equation will be as follows; Total amount of coffee to be made is: x+y=5.........i The percentage amount will be: 0.2x+0.8y=0.6*5 0.2x+0.8y=3.......ii from eqn i y=5-x.......iii substituting iii in ii we get 0.2x+0.8(5-x)=3 0.2x+4-0.8x=3 solving for x we get: 0.2x-0.8x=3-4 -0.6x=-1 thus x=1/0.6 x=5/3 y=5-x y=5-5/3=10/3 thus the amount of x mixed is 5/3 lb and that of y is 10/3 lb
