mixture tables- A candy mixture is to be made from chocolate costing $5 per pound and sugar candies costing $2 per pound. If a total mixture of 50 pounds of mixture is required at a cost of $3 per pound, how much of each must go into the mixture?

Question

mixture tables- A candy mixture is to be made from chocolate costing $5 per pound and sugar candies costing $2 per pound.  If a total mixture of 50 pounds of mixture is required at a cost of $3 per pound, how much of each must go into the mixture?

anonymous · Answer

Define your variables:
let C=number pounds of chocolate
let S=number of pounds of sugar candies

Then the variables can be related according to total weight:  
C+S=50
they may also be related according to cost:
5C+2S=3(C+S), which reduces to 2C=S

Sove the following system by substitution method
C+S=50   [1]
2C=S        [2]

Substitute equation [2] into equation [1], and solve for C:
C+2C=50
C=50/3

Substutute the value for C into [1] to find S:
S=2(50/3)=100/3

Thus, to get 50 pounds of the candy blend at $3/lb, you would need 50/3 or 16 2/3 pounds of chocolate and 100/3 or 33 1/3 pounds of sugar candies.