Solve the problem.
-Ellen wishes to mix candy worth $1.57 per pound with candy worth $3.69 per pound to form 26 pounds of a mixture worth $3.04 per pound. How many pounds of the more expensive candy should she use?
A)8 pounds
B)18 pounds
C)23 pounds
D)10 pounds

Question

Quizplus · Accepted Answer

To solve this problem, we can use the concept of weighted averages. Let $x$ be the amount of the more expensive candy ($3.69 per pound) that Ellen uses, and $26 - x$ will then be the amount of the cheaper candy ($1.57 per pound). The total cost of the mixture can be represented as $3.69x + 1.57(26 - x)$, and this should equal the total cost of the final mixture, which is $3.04 \times 26$. Setting up the equation:$$3.69x + 1.57(26 - x) = 3.04 \times 26$$Solving this equation for $x$ gives the amount of the more expensive candy needed. Simplifying and solving for $x$ yields:$$3.69x + 40.82 - 1.57x = 79.04$$$$2.12x = 38.22$$$$x = 18$$Therefore, Ellen should use 18 pounds of the more expensive candy.

Solve the Problem. -Ellen Wishes to Mix Candy Worth $1.57 Per Pound with Per