Let's state what we know: both fatcontent chocolates added together will be 200 kg
Let's let x = the 20% fatcontent chocolate, and y = the 40% fatcontent chocolate (but we could use any 2 letters or symbols)
So we know that x + y = 200
Let's state the percentages as decimals: 20% = 0.20, 40% = 0.40, and 37% = 0.37
We also know that the 200KG will be a 37% blend, so that's (0.37)(200) = 74
So now we can add the components together to get that blend: 0.20X + 0.40y = 74
Now we have two equations, each using the same x and y
We can solve for either x or y in one of these and substitute back into the other equation. x + y = 200 looks easier, so let's solve it for x: x = 200  y
Now put that x into the other equation: (0.20)(200  y) + (0.40y) = 74
40  0.20y + 0.40y = 74
40 + 0.20y = 74; 0.20y = 34; y = 170kg
x + y = 200; x + 170 = 200; x = 200  170; x = 30kg
So you need only 30KG of 20% fatcontent chocolate, but 170KG of 40% fatcontent chocolate. A commonsense look at the original question shows that makes sense: the 37% result we want is much closer to 40% than to 20%
1/4/2013

Bill F.