Question

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?

Answer 1

Let the weights of the two candies be repres. by x and y.

Then x + y = 60, or x = 60 - y

($1.16 / lb) x + ($0.86 / lb) y = ($1.00 / lb) (60 lb) = $60

Then 1.16(60-y) + 0.86y = 60
69.6 - 1.16y + 0.86y = 60 9.6
9.6 = 0.3y Solving for y, y = ------- = 32 lb
0.3

Then x = (60-32) lb = 28 lb

Answer 2

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

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)
`x+y=60`

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,
`(1.6x+0.86y)/(60) =1`

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)

`0.3x =8.4\\\\x=28`

Substitute into equation (1):

`28+y=60`

`y=32`

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