Question
A candy distributor needs to mix a 40% fat-content chocolate with a 60% fat content chocolate to create 200 kilograms of a 51% fat content chocolate. How many kilograms of each kind of chocolate must they use?
Answers
GPT 3.5
Let's assume the distributor needs to use x kilograms of the 40% fat-content chocolate.
Since the total amount of chocolate needed is 200 kilograms, the distributor will use (200 - x) kilograms of the 60% fat-content chocolate.
To find the total fat content in the mix, you need to calculate the sum of the fat content from each type of chocolate. The fat content of the 40% fat-content chocolate is 0.4x, and the fat content of the 60% fat-content chocolate is 0.6(200 - x).
Since the total mass of the mix is 200 kilograms and the desired fat content is 51%, the equation for the total fat content of the mix is: 0.4x + 0.6(200 - x) = 0.51 * 200.
Simplifying the equation:
0.4x + 0.6 * 200 - 0.6x = 0.51 * 200.
0.4x + 120 - 0.6x = 102.
0.4x - 0.6x = 102 - 120.
-0.2x = -18.
x = -18 / -0.2.
x = 90.
So, the distributor must use 90 kilograms of the 40% fat-content chocolate and (200 - 90) = 110 kilograms of the 60% fat-content chocolate.
Since the total amount of chocolate needed is 200 kilograms, the distributor will use (200 - x) kilograms of the 60% fat-content chocolate.
To find the total fat content in the mix, you need to calculate the sum of the fat content from each type of chocolate. The fat content of the 40% fat-content chocolate is 0.4x, and the fat content of the 60% fat-content chocolate is 0.6(200 - x).
Since the total mass of the mix is 200 kilograms and the desired fat content is 51%, the equation for the total fat content of the mix is: 0.4x + 0.6(200 - x) = 0.51 * 200.
Simplifying the equation:
0.4x + 0.6 * 200 - 0.6x = 0.51 * 200.
0.4x + 120 - 0.6x = 102.
0.4x - 0.6x = 102 - 120.
-0.2x = -18.
x = -18 / -0.2.
x = 90.
So, the distributor must use 90 kilograms of the 40% fat-content chocolate and (200 - 90) = 110 kilograms of the 60% fat-content chocolate.