Formula

Tim kirby

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Joined
Dec 15, 2019
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1
Ok I need a formula lol
Alright I have 2 silos full of coal. #1 silo has 10,000 tons of coal that has an average of 17.52 ash content. #2 silo has 9,652 tons with an average of 9.97 ash. Ok we are loading a train and the customer wants a 14.50 total ash with 12,500 tons loaded on the train. Ok how much will I need to pull out of each silo to get an average of 14.50 ash? I know by plugging and unplugging I’ll need to pull 60% out of #1 silo and 40% out of #2 silo. But I need a formula to use in the future because every train and every blend will be different. I’ve been up all night trying to figure it out. I give up lol. If you can help it would be greatly appreciated. Please and thank you.
 
Ok I need a formula lol
Alright I have 2 silos full of coal. #1 silo has 10,000 tons of coal that has an average of 17.52 ash content. #2 silo has 9,652 tons with an average of 9.97 ash. Ok we are loading a train and the customer wants a 14.50 total ash with 12,500 tons loaded on the train. Ok how much will I need to pull out of each silo to get an average of 14.50 ash? I know by plugging and unplugging I’ll need to pull 60% out of #1 silo and 40% out of #2 silo. But I need a formula to use in the future because every train and every blend will be different. I’ve been up all night trying to figure it out. I give up lol. If you can help it would be greatly appreciated. Please and thank you.
Suppose you

withdraw W1 pounds of coal from silo1 ..

The amount of ash in W1 = 0.1752 * W1

To make total 12500 tons, we will need to draw (12500 - W1) = W2

The amount of ash in W2 =?

Total ash allowed in the mixture of 12500 tons = ?

Continue.....
 
\(\displaystyle
\text{Let $x_1$ be the amount of coal pulled from silo #1, and $x_2$ the amount from silo #2, in tons}\\
\text{The total amount of ash the customer wants is $12500 \cdot 0.1450 = 1812.5 ~ton$}\\~\\
0.1752x_1 + 0.0997x_2 = 1812.5\\
x_1+x_2 = 12500
\)

Can you solve this set of equations to obtain your formula for \(\displaystyle x_1,~x_2\) ?
 
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