A grocer wants to mix nuts costing $5 per kg with nuts costing $8 per kg to make a 10 kg mixture selling for $6 per kg. How much of each type should be mixed?

Question

A grocer wants to mix nuts costing $5 per kg with nuts costing $8 per kg to make a 10 kg mixture selling for $6 per kg.  How much of each type should be mixed?

How do I set up this problem?  Thank you.

bobpursley · Answer

let E be weight of expensive nuts, C be cheaper nuts
E*8+C*5=10*6 value equation
E+C=10 mass equation

Solve it by any method, I will do determinants

Det: 8-5=3
E= (60-50)/3=10/3 =3.33 lb
C= 80-60 /3=20/3 =6.66 lb