I have a world problem question. Which is substitution i think, i really don't know, that's why I am struggling.

Question

Lyle needs 200g of chocolate that is 86% cocoa for a cake recipe. He has one kind of chocolate that is 99% cocoa and another kind that is 70% cocoa. Determine how much of each kind chocolate is needed to make the new type of chocolate.

Answer 1

 

How to mix 99% cocoa and 70% cocoa to get 200 g of 86% cocoa

(x g)(95%) + (200g - xg)(70%) = (200 g) (86%)

95x + 14,000 - 70x = 17,200

25x = 3200

x = 128

So, you need 128 g of the chocolate that is 95% cocoa and 200-128 g = 72 g of the chocolate that is 70% cocoa.

CHECK:  128 g x 0.95 = 121.6 g cocoa

72 g x 0.70 = 50.4 g cocoa

total g cocoa = 172g

172 g cocoa/200 g = 0.86 = 86% cocoa