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?
28 pounds of the candy costing $1.16 and 32 pounds of the candy costing $0.86.
We have two types of candy. Let
We want to end up with 60 pounds of candy so we know that:
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
We can rearrange that to get a second equation:
multiply equation (1) by
Add equation (2) and equation (3), the
divide through by 0.3:
Substitute into equation (1):
So we want 28 pounds of the candy costing $1.16 and 32 pounds of the candy costing $0.86.