Question

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

Hailey's mixing two different coffee blends.  Represent them by x and y (in pounds).  Then x + y = 5 lb, and x = 5 - y.

How much pure Sum. beans are we talking about here?

0.20x + 0.80y = 0.60(5 lb)  Mult all 3 terms by 100 to remove fractions:

20x + 80 y = 300.  Subst. 5-y for x:

20(5-y) + 80y = 300 => 100-20y + 80y = 300 => 60y = 200, and so
 
                                                                                 y = 20/6 or 10/3 lb
                                              Then x = 5-10/3, or    x =5/3 lb

Use 5/3 lb of the first blend and 10/3 lb of the second blend to come up with 5 lb of a 60% blend.