Question

Evelyn is making a candy that contains 25% dark chocolate and the rest milk chocolate. The candy has 3 pounds of milk chocolate.

Part A: Write an equation using one variable that can be used to find the total number of pounds of dark chocolate and milk chocolate in the candy. Define the variable used in the equation. (5 points)

Part B: How many pounds of dark chocolate are present in the candy? Show your work. (5 points)

Answer 1

Part A:

Let c represent the total amount of chocolate there is in lbs.

c = 0.25c + 0.75c

Part B:

0.75c represents milk chocolate, and we know that there are 3 lbs of milk chocolate, so you can replace the 0.75c with 3 (representing 3 lbs):

c = 0.25c + 3

Divide all the terms by c:

1 = 0.25 + 3/c

Subtract 0.25 from both sides to combine the like terms:

0.75 = 3/c

Multiply all the terms by c to make the equation easier to work with:

0.75c = 3

Divide both sides by 0.75 to isolate the c and find the total amount of chocolate in pounds.

c = 4

Substitute c for 4 in the term that defines dark chocolate (which was 0.25c)

0.25(4) = 1 pound

Therefore, there was exactly 1 pound of dark chocolate present in the chocolate.

This makes sense, as 1 pound of dark chocolate + 3 pounds of milk chocolate = 4 pounds of chocolate in total, and 1 is 25% of 4 and 3 is 75% of 4.