The owner of a candy store want to sell, for $6 per lb, a mixture of chocolate-covered raisina, which usually sells for $3 per lb, and chocolate-covered macadamia nuts, which usually sells for $8 per lb. They have 40 lbs of raisins. How many lbs of the nuts should be mix with the raisins so that they hit their target value of $6 per lb mixture?
To find the number of pounds of nuts that need to be mixed with the raisins to hit the target value of $6 per pound mixture, we can form the following equation:
(Quantity of raisins * Price of raisins) + (Quantity of nuts * Price of nuts) = (Total quantity of mixture * Target price)
Let's denote:
Quantity of raisins = x (40 lbs)
Price of raisins = $3 per lb
Quantity of nuts = y (unknown)
Price of nuts = $8 per lb
Total quantity of mixture = x + y (lbs)
Target price = $6 per lb
Now, let's substitute the values into the equation:
(40 * 3) + (y * 8) = (x + y) * 6
Simplifying:
120 + 8y = 6x + 6y
Rearranging:
120 = 6x - 2y
To solve for y, we need to determine the value of x. We know that x = 40 lbs, so:
120 = 6 * 40 - 2y
120 = 240 - 2y
2y = 240 - 120
2y = 120
y = 120/2
y = 60
Therefore, 60 pounds of nuts should be mixed with the 40 pounds of raisins to hit the target value of $6 per pound mixture.