Question

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

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.