<em>Part A: </em>
Let c represent the total amount of chocolate there is in lbs.
c = 0.25c + 0.75c
<em>Part B: </em>
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.
