Question

PLEASE HELP

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. 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)