A candy distributor needs to mix a 10% fat-content chocolate with a 40% fat-content chocolate to create 100 kilograms of a 28% fat-content chocolate. How many kilograms of each kind of chocolate must they use?

We will use 40 kilograms of 10% chocolate

There are 60 kilograms of 40% chocolate

Step-by-step explanation:

We add. 10% chocolate to 40% chocolate to get 28% chocolate

We have a total of 100 kilograms of 28% chocolate

Let x be the kilograms of the 10 %

For a total of 100 kilograms, we will add (100-x) of the 40 %

The percentage * the weight + percentage * weight = Final percentage * weight

.10 * x +.40 * (100-x) =.28 * 100

Disribute

.10x + 40 -.4x = 28

Combine like terms

-.3x + 40 = 28

Subtract 40 from each side

-.3x + 40-40 = 28-40

-.3x = - 12

Divide each side by -.3

-.3x/-.3 = - 12/-.3

x = 40

We will use 40 kilograms of 10% chocolate

We need to find the kilograms of 40% chocolate

There is a total of 100 kilograms, so 100-40 = 60

There are 60 kilograms of 40% chocolate