Question

The Sweet Shoppe wishes to sell a special mix for Valentine’s Day that consists of Dark Chocolate that costs $4.00 per lb and Milk Chocolate that costs $2.00 per lb. How much of each should be used to get a 50 lb mix that costs $2.60 per lb?

Answer 1

Answer: Quantity of Dark Chocolate used = 15 lb

Quantity of Milk Chocolate used = 35 lb

Explanation:

Let x = Quantity of Dark Chocolate.

y = Quantity of Milk Chocolate.

As per given , we have the following system of equations:

`x+y= 50-------------(1)\\\\ 4x+2y=50*2.60\\\\ 4x+2y=130-----------(2)`

Multiply equation (1) by 2 , we get

`2x+2y= 100-------(3)`

Eliminate equation (3) from equation (2) , we get

`2x=30\\\Rightarrow\ x=15`

Put x= 15 in (1) , we get
`15+y=50`

⇒ y=35

Therefore , Quantity of Dark Chocolate used = 15 lb

Quantity of Milk Chocolate used = 35 lb