Help with mixture problem

Question

A candy distributor needs to mix a 10% fat-content chocolate with a 60% fat-content chocolate to create 150 kilograms of a 46.7% fat-content chocolate. How many kilograms of each kind of chocolate must they use?

A) Write an equation that uses the information as it is given above that can be used to solve this problem. Use x as your variable to represent the quantity of 10% fat-content chocolate.

Answer 1

To solve this problem, we can set up a system of equations based on the given information.

We're told what we are solving for in the problem (the quantity in kg. of 10% fat-content chocolate). Therefore, let's use x to represent the quantity in kg, of the 10% fat-content chocolate.

The total weight of the mixture is 150 kilograms, so we can simply represent the quantity of the 60% fat-content as 150−x kilograms.

The total fat content in the mixture is 46.7% of 150 kilograms. We can set up an equation that represents the total fat content from both types of chocolate:

1. The 10% fat-content chocolate contributes 0.10x kilograms of fat.
2. The 60% fat-content chocolate contributes 0.60(150−x) kilograms of fat.
3. The total fat content in the mixture is 0.467×150 kilograms.

The equation representing the total fat content is:

0.10x+0.60(150−x)=0.467×150

This equation can be used to solve for x, the quantity of 10% fat-content chocolate needed in the mixture.

Based on the question, we are done here. However, if asked to solve:

After the first round of simplifying, we get:

0.1x + 90 - 0.6x = 70.05

After isolating x and rearranging terms:

-0.5x = 19.95

Dividing both sides by -0.5:

x = 39.9 kg of 10% chocolate.

Answer 2

0.10x + 0,60(150 - x) = 0.467(150)

Solve for x.