10% fat-content chocolate with a 50% fat-content chocolate to create 200 kilograms of a 12% fat-content kilograms of each kind of chocolate must they use?

Question

A candy distributor needs to mix a 10% fat-content chocolate with a 50% fat-content chocolate to create 200 kilograms of a 12% fat-content chocolate. How many kilograms of each kind of chocolate must they use?

Answer 1

Amount of 10% fat-content chocolate=x

amount of 50% fat-content chocolate =y

 

 

x + y =200 ____________ eq 1

 

so x =200 -y

 

10 % of x + 50 % of y = 12 % of (x +y)

 

0.1 x + 0.5 y = 0.12(x+y)

0.1 x+0.5y =0.12x +0.12y

 

0.02x - 0.38 y =0  ____________ eq 2

 

 

substitute x = 200 -y  in eq 2

 

0.02(200-y) -0.38y =0

 

4 -0.02 y -0.38y =0

 

4 -0.4y=0

0.4 y = 4

y =4/0.4 = 10

 

x =200 -10 =190

 

Amount of 10% fat-content chocolate=x =190 kg
amount of 50% fat-content chocolate =y = 10 kg