Question

A candy distributor needs to mix a 20% fat-content chocolate with a 40% fat-content chocolate to create 100 kilograms of a 34% fat-content chocolate. How many kilograms of each kind of chocolate must they use?

Answer 1

30 kilograms of the 20% fat-content chocolate was mix with 70 kilograms of the 40% fat-content chocolate

Step-by-step explanation

Let the amount of the 20% fat-content chocolate mixed be x.

Let the amount of the 40% fat-content chocolate mixed be y.

100 kilograms of the 34% fat-content chocolate was created, so:

x + y = 100 _____(1)

The 20% fat-content chocolate and the 40% fat-content chocolate were mixed to create a 34% fat-content chocolate.

This means that:

20 * x + 40 * y = 100 * 34

=> 20x + 40y = 3400 _____(2)

From (1):

x = 100 - y

Put that in (2):

20(100 - y) + 40y = 3400

2000 - 20y + 40y = 3400

2000 + 20y = 3400

Collect like terms:

20y = 3400 - 2000 = 1400

y = 1400 / 20

y = 70 kilograms

Recall that:

x = 100 - y

=> x = 100 - 70

x = 30 kilograms

Therefore, 30 kilograms of the 20% fat-content chocolate was mix with 70 kilograms of the 40% fat-content chocolate.