Recipe Ingredients to manufacture widget

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Discussion Overview

The discussion revolves around the calculation of ingredient quantities needed to manufacture a specific number of units of widget XYZ from a given recipe. Participants explore the relationships between the ingredients and the final product weight, focusing on proportions and ratios.

Discussion Character

  • Homework-related, Mathematical reasoning, Debate/contested

Main Points Raised

  • One participant presents a recipe with specific ingredient weights and asks how much of each ingredient is needed to produce 80 units of widget XYZ.
  • Another participant suggests using proportions to determine the required amounts, calculating the ratio of ingredient AAA in the mixed product.
  • There is a question about the interpretation of "80 units," with one participant assuming it refers to 80 kg, while another clarifies that widget XYZ consists of 100 grams of widget.
  • Participants discuss the possibility of simplifying calculations by expressing the amount of AAA in terms of a single formula.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the interpretation of "80 units" and whether it refers to weight or quantity. There is no consensus on the correct interpretation or the resulting calculations.

Contextual Notes

There are unresolved assumptions regarding the definition of a unit of widget XYZ and the implications for the calculations. The discussion reflects varying interpretations of the problem statement.

Who May Find This Useful

Individuals interested in mathematical reasoning related to proportions and ingredient calculations in manufacturing contexts may find this discussion relevant.

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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