Recipe Ingredients to manufacture widget

[MathsNotSoGood]

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

 

[earboth]

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 \(\displaystyle \frac1{800}\)-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: \(\displaystyle r(AAA)=\frac{0.16}{99.84} \cdot 0.1\)

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

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

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.

 

[MathsNotSoGood]

Many thanks
Where do you getbthe 80 kg from?

 

[earboth]

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:

\(\displaystyle a(AAA)=\underbrace{\frac{{\color{red}0.16}}{99.84} \cdot 0.1}_{\text{this is r(AAA)}} \cdot 800 = \frac{80}{99.84} \cdot 0.16\)

 

[MathsNotSoGood]

Thanks
widget XYZ consists of 100 grams of widget so it's weight is 100 grams

Thank you