Answer:
The kilograms of chocolate for the 40% fat content (1st chocolate) = 90kg
The kilograms of chocolate for the 50% fat content (2nd chocolate) = 10kg
Step-by-step explanation:
A candy distributor needs to mix a 40% fat-content chocolate with a 50% fat-content chocolate to create 100 kilograms of a 41% fat-content chocolate. How many kilograms of each kind of chocolate must they use?
Let us represent
Kilograms of first chocolate = x
Kilograms of second chocolate = y
A candy distributor needs to mix a 40% fat-content chocolate with a 50% fat-content chocolate to create 100 kilograms of a 41% fat-content chocolate.
Hence:
40% × x + 50% × y = 41% × 100
0.40x + 0.50y = 0.41× 100
0.40x + 0.50y = 41.......Equation 1
x + y = 100kg ......Equation 2
x = 100 - y
Substitute 100 - y for x
0.40(100 - y) + 0.50y = 41
40 - 0.40y + 0.50y = 41
Collect like terms
- 0.40y + 0.50y = 41 - 40
0.10y = 1
y = 1/0.1
y = 10.
Therefore, the kilograms of chocolate for the 50% fat content (2nd chocolate) = 10kg
Remember:
x = 100 - y
x = 100kg - 10kg
x = 90kg
The kilograms of chocolate for the 40% fat content (1st chocolate) = 90kg
