How much candy at $1.16 a pound should be mixed with candy worth 86¢ a pound in order to obtain a mixture of 60 pounds of candy worth a dollar a pound? How much candy at$1.16 a pound should be mixed with candy worth 86¢ a pound in order to obtain a mixture of 60 pounds of candy worth a dollar a pound? I don't even know where to begin on this one.

Jan 13, 2018

28 pounds of the candy costing $1.16 and 32 pounds of the candy costing$0.86.

Explanation:

We have two types of candy. Let $x$ be the candy costing $1.16 a pound. Let $y$be the candy costing$0.86 per pound. (We'll work in dollars for the problem.)

We want to end up with 60 pounds of candy so we know that:

Equation (1): $x + y = 60$

We know that we want the average cost to be $1 per pound. To get the average cost we need to know the total cost and divide by the total pounds. Total cost: 1.16x + 0.86y Total pounds: 60 Average cost we want: 1 So, $\frac{1.16 x + 0.86 y}{60} = 1$We can rearrange that to get a second equation: Equation (2): $1.16 x + 0.86 y = 60$multiply equation (1) by $- 0.86$to get equation (3): Equation (3): $- 0.86 x - 0.86 y = - 51.6$Add equation (2) and equation (3), the $y$cancels out: $0.3 x = 8.4$divide through by 0.3: $x = 28$Substitute into equation (1): $28 + y = 60 \rightarrow y = 32$. So we want 28 pounds of the candy costing$1.16 and 32 pounds of the candy costing \$0.86.