How much candy at $1.16 a pound should be mixed with candy worth 86 cent 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.

Step-by-step explanation:

To Find: How much candy at $1.16 a pound should be mixed with candy worth 86 cent a pound in order to obtain a mixture of 60 pounds of candy worth a dollar a pound?

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.)

So we know that:

Equation (1)

Now we want the average cost to be $1 per pound.

So,To get the average cost we need to know the total cost and divide by the total pounds.

Total cost: 1.16x + 0.86y

Since Total pounds: 60

Average cost : 1

So,  

Equation (2):  

multiply equation (1) by  −0.86  to get equation (3):

Equation (3):  

Add equation (2) and equation (3)

Substitute into equation (1):  

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

2

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