Solve the problem.
-The owners of a candy store want to sell, for $6 per pound, a mixture of chocolate-covered raisins, whichusually sells for $3 per pound, and chocolate-covered macadamia nuts, which usually sells for $8 perpound. They have a 70-pound barrel of the raisins. How many pounds of the nuts should they mix withthe barrel of raisins so that they hit their target value of $6 per pound for the mixture?
A)105 lb
B)98 lb
C)91 lb
D)112 lb

Question

Quizplus · Accepted Answer

To solve this, we use the concept of weighted averages. Let $x$ be the pounds of nuts needed. The total cost of the raisins is $70 \times 3 = 210$ dollars. The total cost of the nuts is $8x$ dollars. The total weight of the mixture is $70 + x$ pounds, and the total cost of the mixture is $210 + 8x$ dollars. We want the cost per pound to be $6, so we set up the equation $\frac{210 + 8x}{70 + x} = 6$. Solving for $x$, we get $210 + 8x = 420 + 6x$, which simplifies to $2x = 210$, giving $x = 105$. Therefore, 105 pounds of nuts are needed.

Solve the Problem. -The Owners of a Candy Store Want to Sell, for to Sell