A candy distributor needs to mix a 10% fat-content chocolate with a 30% fat-content chocolate to create 100 kilograms of a 26% fat-content chocolate. How many kilograms of each kind of chocolate must they use?
Kilograms of the 10% chocolate and
Kilograms of the 30% chocolate.
Let x be the kilograms of the 10% chocolate and y be the kilograms of the 30% chocolate.
We know that the total weight of the mixture is 100 kilograms, so we have the equation x + y = 100.
We also know that the fat content in the mixture is 26%, so we have the equation (0.1x + 0.3y) / 100 = 0.26.
To solve this system of equations, we can use substitution. First, solve the first equation for x: x = 100 - y.
Now substitute this expression for x in the second equation: (0.1(100 - y) + 0.3y) / 100 = 0.26.
Simplify and solve for y: (10 - 0.1y + 0.3y) / 100 = 0.26.
(10 + 0.2y) / 100 = 0.26.
10 + 0.2y = 0.26 * 100.
10 + 0.2y = 26.
0.2y = 26 - 10.
0.2y = 16.
y = 16 / 0.2.
y = 80.
Now substitute this value for y in the equation x + y = 100: x + 80 = 100.
x = 100 - 80.
x = 20.
Thus, the distributor needs to use 20 kilograms of the 10% chocolate and 80 kilograms of the 30% chocolate.