Question

How many pounds of candy selling for $1.50 a pound should be added to six pounds of candy selling for $ 3.75 a pound to create a blend, which will sell for $2.85 a pound?

Answer 1

To find the right amount of $1.50 per pound candy to mix with 6 pounds of $3.75 per pound candy to get a blend that costs $2.85 per pound, we use a weighted average calculation. We set up an equation and solve for x, which yields that 4 pounds of the $1.50 candy should be added.

Step-by-step explanation:

To solve the problem of mixing candies to achieve a desired blend price, we can use a weighted average. In this case, the equation to determine the amount of candy at $1.50 per pound to blend with 6 pounds at $3.75 a pound to achieve a final price of $2.85 per pound is as follows:

($1.50 × x) + ($3.75 × 6) = ($2.85 × (x + 6))

Solving this equation involves distributing the $2.85 on the right side:

$1.50x + $22.50 = $2.85x + $17.10

Now, we need to combine like terms by moving all the terms involving x to one side and constants to the other:

$22.50 - $17.10 = $2.85x - $1.50x

This simplifies to:

$5.40 = $1.35x

Then, divide both sides by $1.35 to find x:

x = $5.40 / $1.35

x = 4

Therefore, 4 pounds of candy selling for $1.50 per pound should be added to achieve the desired blend.