Question

how many lbs of candy that sells for $3.25 per pound must be mixed with candy that sells for $1.75 per pound to obtain 10 pounds of a mixture that should sell for $2.50 per pound.

Answer 1

To create a 10-pound mixture of candy selling for $2.50 per pound, 5 pounds of candy priced at $3.25 per pound must be mixed with 5 pounds of candy priced at $1.75 per pound.

Step-by-step explanation:

To solve this problem, we can use the concept of a weighted average to find out how many pounds of candy at each price point need to be combined to reach a desired average price for the mixture. In this case, we want to mix candy that is $3.25 per pound with candy that is $1.75 per pound to create a 10-pound mixture that will sell for $2.50 per pound.

Let's denote the amount of the $3.25 candy as x pounds and the amount of the $1.75 candy as y pounds. We are looking for the values of x and y such that:

• The total weight of the mixture is 10 pounds: x + y = 10
• The total cost of the mixture should equal the cost of 10 pounds at $2.50 per pound: 3.25x + 1.75y = 10 \times 2.50

Solving this system of equations, first multiply the second equation by 100 to avoid decimals:

• 325x + 175y = 2500

Now subtract the first equation, multiplied by 175, from this new equation:

325x + 175y - 175x - 175y = 2500 - 1750

This simplifies to 150x = 750, and solving for x gives us x = 5 pounds.

Since x + y = 10, we have y = 10 - 5 = 5 pounds. Therefore, 5 pounds of the $3.25 candy must be mixed with 5 pounds of the $1.75 candy to obtain 10 pounds of a mixture that will sell for $2.50 per pound.