ANSWER: 200
Step-by-step explanation:
Let x represent the amount of second chocolate that should be added.
First, 300 pounds of chocolate
1 to 7 = chocolate to caramel
Hence there are a total of eight pieces (1+7=8).
There are:
1/8 300 pounds cocoa
7/8 300 pounds caramel
Second chocolate: x pounds cocoa to caramel = 1 to 15 Hence, there are in total 16 parts (1+ 15 = 16)
There are:
Caramel: 15/16" x pounds Cocoa: 1/16" x pounds
Chocolate yield: 300 + x pounds
1 to 9 = chocolate to caramel
As a result, there are a total of ten pieces (1 + 9 = 10)
There are:
1/10 (300 + x) pound cocoa
9/10 (300 + x) pounds caramel
Because there is only one part cocoa in every chocolate, adding up the amounts of cocoa is simple:
1/8* 300+ 1/16* x = 1/10 * (300 + x)
300/8 + x/16 300/10 + x/10 =
75/2 + x/16 = 30 + x/10
75/230= x/10 - x/16
75/2 - 60/2 = 8x/80 - 5x/80
(75 - 60)/2 = (8x - 5x)/80
15/2 = 3x/80
80 15/2 = 3x
40 * 15 = 3x
600 = 3x
x = 600/3
200 pounds = x
As a result, the answer is 200.