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.

1 Answer
Jan 13, 2018

Answer:

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, #(1.16x + 0.86y)/60=1#

We can rearrange that to get a second equation:

Equation (2): #1.16x + 0.86y = 60#

multiply equation (1) by #-0.86# to get equation (3):

Equation (3): #-0.86x -0.86y =-51.6#

Add equation (2) and equation (3), the #y# cancels out:

#0.3x= 8.4#

divide through by 0.3:

#x = 28#

Substitute into equation (1): #28+y=60 rarr y=32#.

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