Question

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. 

Answer 1

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

Answer 2

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.