SOLUTION: A candy distributor needs to mix a 10% fat-content chocolate with a 60% fat-content chocolate to create 200 kilograms of a 12.5% fat-content chocolate. How many kilograms of each k

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Question 791474: A candy distributor needs to mix a 10% fat-content chocolate with a 60% fat-content chocolate to create 200 kilograms of a 12.5% fat-content chocolate. How many kilograms of each kind of chocolate must they use?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
This is a mixture problem.

First, assign variables to everything:
H = 60% fat
T = 12.5% fat
L = 10% fat
M = 200 kilograms
u = unknown amount of the 10% fat candy
v = unknown amount of the 60% fat candy

Form the equations to describe the system:
%28Lu%2BHv%29%2FM=T and u%2Bv=M

Solve the system for u and v.
v=M-u.
Substitute.
Lu%2BH%28M-u%29=MT
Lu%2BHM-Hu=MT
Lu-Hu%2BHM=MT
%28L-H%29u%2BHM=MT
%28L-H%29u=MT-MH
u=%28MT-MH%29%2F%28L-H%29
highlight%28u=M%28T-H%29%2F%28L-H%29%29 --------just watch the signs carefully.
And conclude for the other quantity, highlight%28v=M-M%28T-H%29%2F%28L-H%29%29

Now just substitute given values to find values of u and v.