Question

A candy company wants to produce 30 kilograms of a special 25​% fat content chocolate to confirm with customer dietary demands. To obtain​ this, a​ 50% fat content imported chocolate is combined with a 20​% fat content domestic chocolate in a special melting process. How many kilograms of the​ 50% fat content chocolate and how many kilograms of the 20​% fat content chocolate are used to make the required 30 ​kilograms?

a) 15 kg of 50% chocolate and 15 kg of 20% chocolate

b) 20 kg of 50% chocolate and 10 kg of 20% chocolate

c) 10 kg of 50% chocolate and 20 kg of 20% chocolate

d) 25 kg of 50% chocolate and 5 kg of 20% chocolate

Answer 1

To create 30 kg of 25% fat content chocolate, 10 kg of 50% fat content chocolate and 20 kg of 20% fat content chocolate should be mixed. This is calculated by setting up and solving a system of linear equations based on total weight and fat content.

Step-by-step explanation:

To find out how many kilograms of the 50% fat content chocolate and the 20% fat content chocolate are needed to make 30 kilograms of a special 25% fat content chocolate, we can set up a system of linear equations. Let's use x to represent the kilograms of the 50% chocolate and y to represent the kilograms of the 20% chocolate. The first equation will represent the total weight of the final mixture, and the second will represent the total fat content of the mixture. We have:

• x + y = 30 (total weight of the chocolate)
• 0.5x + 0.2y = 0.25*30 (total fat in the chocolate)

Solving these equations gives us x = 10 kg and y = 20 kg. This means the company should use 10 kg of the 50% fat chocolate and 20 kg of the 20% fat chocolate to achieve the desired 25% fat content in the 30 kg mixture.

Therefore, the correct answer is: c) 10 kg of 50% chocolate and 20 kg of 20% chocolate.