MHB Determining ratio of a 2 part mix

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The discussion focuses on determining the percentage composition of a sand mix in a foundry, specifically the ratio of mechanically reconditioned sand to thermally reclaimed sand. Given the weights of each sand type and the overall mix, the equations M + T = 100 and 850M + 889T = 87800 are used to solve for the percentages. The solution reveals approximately 28.2% mechanical and 71.8% thermal sand in the mix. Participants express gratitude for the mathematical clarification, noting its practical application in the foundry setting. The conversation highlights the importance of accurate mix calculations for operational efficiency.
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Mechanically reconditioned sand weighs 8.50#/gallon
Thermally reclaimed sand weighs 8.89#/gallon
A mix of these two kinds of sand weighs 8.78#/gallon
What is the % thermal and %mechanical in the mix?

I work in a foundry and we feed these two types of sand into a hopper that feeds a mixer. It's important to have a quick and reliable test that can be done on the shop floor that confirms that the mix is 60/40 or 70/30 etc.

I looked at a lot of calculators and examples online but didn't find any that fit the data I have collected. I sure would appreciate some help. Anyone want to set me straight on this? Thx
 
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Let's let $M$ be the percentage of mechanically reconditioned sand and $T$ be the percentage of thermally reconditioned sand.

So, we know that:

$$M+T=100$$

And we also know:

$$850M+889T=87800$$

Solving this system, we find:

$$M=\frac{1100}{39}\approx28.2,\,T=\frac{2800}{39}\approx71.8$$

You could also state:

$$M:T=11:28$$
 
modern day (math) warrior, mean mean stride...
thank you. I can duplicate that but I don't fully understand it yet.
I get the 850M + 889T = 87800
can you show me a little more about how you got to the rest?
much appreciated.
 
Suppose we take the first equation:

$$M+T=100$$

and multiply it by $-850$, so that it becomes:

$$-850M-850T=-85000$$

Now, recall we have:

$$850M+889T=87800$$

Adding these two equation, we will eliminate $M$, to get:

$$39T=2800$$

which gives us:

$$T=\frac{2800}{39}$$

And then taking the original first equation, and using this value for $T$, we have:

$$M=100-\frac{2800}{39}=\frac{1100}{39}$$
 
There it is! I guess this answers the age old question "Why do I have to learn this- I'll never use it." Math in the foundry... I thank you.
I still have some R&R concerns regarding sampling technique but we can easily test and measure that. The roadblock was the calculation of the mix and you have cleared that right up.
 
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