Question

house blend coffee is 50% columbian beans and special blend coffee is 80% columbian beans. how much of each should be used to produce 100 kg of a blend that is 68% columbian beans

Answer 1

Let house blend be H and special blend be S.

eq 1 ----- H+S=100

eq 2 ----- as the percentages are 50 and 80 respectively,
50%H+80%S=68%
0.5H+0.8S=68

solve the equations simultaneously.
eq 1 ------ S=100-H
Substituting in eq 2
0.5H+0.8(100-H)=68
0.5H+80-0.8H=68
-0.3H=-12
H=40kg

S=100-H=60kg