How much dark chocolate should be added to make a ripple blend that is 35% fat?

Question

The chocolate factory makes a dark chocolate that is 31% fat and a white chocolate that is 47% fat. How many kilograms of dark chocolate should be mixed with 300 kilograms of white chocolate to make a ripple blend that is 35% fat?

Answer 1

Let W be the weight of white chocolate and D be the weight of dark chocolate.

 

W + D is the weight of the blend.

 

W = 300

 

D(.31) + 300(.47) = (D + 300)(.35)

 

Multiply by 100 to clear the fractions

 

31D + 300(47) = 35(D + 300)

 

31D + 14100 = 35D + 10500

 

3600 = 4D

 

D = 900

 

900 kilograms of the dark chocolate needs to be mixed with the white.