A candy distributor needs to mix a 40% fat-content chocolate with a 60% fat-content chocolate to create 100 kilograms of a 40% fat-content chocolate. How many kilograms of each kind of chocolate must they use?

Let's assume that the distributor needs to use x kilograms of the 40% fat-content chocolate and y kilograms of the 60% fat-content chocolate.

We know that the total weight of the mixture is 100 kilograms, so x + y = 100.

Since the desired fat content of the mixture is 40%, we can set up the equation for the fat content as:

(0.40)(x) + (0.60)(y) = (0.40)(100).

Now we can solve these two equations simultaneously to find the values of x and y.

From the first equation, we can solve for y:

y = 100 - x.

Substituting this into the second equation, we have:

(0.40)(x) + (0.60)(100 - x) = (0.40)(100).

Simplifying the equation, we get:

0.40x + 60 - 0.60x = 40.

Combining like terms, we have:

-0.20x + 60 = 40.

Subtracting 60 from both sides, we get:

-0.20x = -20.

Dividing both sides by -0.20, we get:

x = 100.

Substituting this value of x back into the first equation, we have:

y = 100 - x = 100 - 100 = 0.

Therefore, the distributor needs to use 100 kilograms of the 40% fat-content chocolate and 0 kilograms of the 60% fat-content chocolate to create a 100-kilogram mixture with a 40% fat content.

Answer: The distributor needs to use 100 kilograms of the 40% fat-content chocolate and 0 kilograms of the 60% fat-content chocolate.