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] This question can be modeled by simultaneous equation this is because the question requires to find the value of two unknowns. It is normally used in the situations where two or more unknown variables are referred to, these unknowns are normally related to each other through equal number of equations that are to be solved in order to obtain finite number of solutions.

b] the solution to the system will first be obtained through forming the equations, these equations are:
x is the amount of 20% blend
y is the amount of 80% blend.
therefore:
x+y=5
hence:
y=5-x...........i
next we have:
0.2x+0.8y=0.6×5....ii
to solve the equations we substitute i in ii as follows:
0.2x+0.8(5-x)=3
0.2x+4-0.8x=3
0.2x-0.8x=3-4
-0.6x=-1
x=5/3
y=5-x=5-5/3=10/3
therefore:
5/3 lb of 20% blend and 10/3 lb of 80% blend.