A candy distributor needs to mix a 30% fat-content chocolate with a 50% fat-content chocolate to create 200 kilograms of a 46% fat-content chocolate. How many kilograms of each kind of chocolate must they use?

Step-by-step explanation:

If x is the kilograms of 30% chocolate, and y is the kilograms of 50% chocolate, then:

x + y = 200

0.30x + 0.50y = 0.46 (200)

Solving the system of equations with substitution:

0.30x + 0.50 (200 - x) = 0.46 (200)

0.30x + 100 - 0.50x = 92

8 = 0.20x

x = 40

y = 200 - x

y = 160

The distributor needs 40 kg of 30% chocolate and 160 kg of 50% chocolate.