# 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? ##### 1 Answer 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.