MHB Recipe Ingredients to manufacture widget

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The discussion revolves around calculating the required amounts of ingredients AAA, BBB, CCC, and DDD to manufacture 80 units of widget XYZ, each weighing 0.1 kg. The initial recipe yields 99.84 kg of widget from the specified ingredient amounts. To find the necessary quantities for 80 units, the user is advised to use proportions based on the ratio of each ingredient in the total mixture. Clarifications were made regarding the weight of the final product, confirming that 80 units correspond to 8 kg, not 80 kg. The calculations can be simplified by applying the ingredient ratios directly to the desired weight of widget XYZ.
MathsNotSoGood
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I am have a bad day and can't see the wood from the trees!

I have the following ingredients in a widget recipe:

AAA 0.16Kg
BBB 0.115Kg
CCC 0.16Kg
DDD 99.405Kg

Mixed together this makes 99.84Kg of widget

I use 0.1Kg of widget above to manufacture widget XYZ

If I want to manufacture 80 units of widget XYZ, how much of ingredients AAA, BBB, CCC & DDD will I need?

Please show calculations!

Many thanks in advance
 
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MathsNotSoGood said:
I am have a bad day and can't see the wood from the trees!

I have the following ingredients in a widget recipe:

AAA 0.16Kg
BBB 0.115Kg
CCC 0.16Kg
DDD 99.405Kg

Mixed together this makes 99.84Kg of widget

I use 0.1Kg of widget above to manufacture widget XYZ

If I want to manufacture 80 units of widget XYZ, how much of ingredients AAA, BBB, CCC & DDD will I need?

Please show calculations!

Many thanks in advance

Good evening,

use proportions:

1. 0.1 kg is the $$\frac1{800}$$-th part of 80 kg. That means you have to multiply the amounts by 800.

2. The ratio of AAA in the ready mixed product is: $$r(AAA)=\frac{0.16}{99.84} \cdot 0.1$$

3. To get the amount of AAA in 80 kg of XYZ you have to calculate:

$$a(AAA)=\underbrace{\frac{{\color{red}0.16}}{99.84} \cdot 0.1}_{\text{this is r(AAA)}} \cdot 800 \approx 0.1282\ kg$$

4. You only have to replace the red value by those given in your question.

5. All 4 results should add up to 80 kg.
 
Many thanks
Where do you getbthe 80 kg from?
 
MathsNotSoGood said:
Many thanks
Where do you getbthe 80 kg from?

Good morning,

you wrote:
I use 0.1Kg of widget above to manufacture widget XYZ

If I want to manufacture 80 units of widget XYZ, how

I was sure that 80 units mean 80 kg. If this is a misinterpretation then you have to tell us what 1 unit could be.

By the way: You probably have noticed that the calculations can be done a little bit shorter:

$$a(AAA)=\underbrace{\frac{{\color{red}0.16}}{99.84} \cdot 0.1}_{\text{this is r(AAA)}} \cdot 800 = \frac{80}{99.84} \cdot 0.16$$
 
Thanks
widget XYZ consists of 100 grams of widget so it's weight is 100 grams

Thank you
 
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