Calculate the Feather Mix Price: Combining 42% Pigeon, 32% Goose, and Ostrich Feathers

Weighted Average with Percentage Compositions

A factory produces a mix of feathers for filling pillows that constitutes 42% pigeon feathers, 32% goose feathers, and the rest are ostrich feathers.

The prices of the feathers per kg are:

FeatherPrice35</text><textx="288"y="351"dominantbaseline="alphabetic"fontfamily="geogebrasansserif,sansserif"fontsize="48"textdecoration="normal">95</text><text x="288" y="351" dominant-baseline="alphabetic" font-family="geogebra-sans-serif, sans-serif" font-size="48" text-decoration="normal">9572$PigeonGooseOstrich

What is the price per kg of the mix?

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1

Understand the problem

A factory produces a mix of feathers for filling pillows that constitutes 42% pigeon feathers, 32% goose feathers, and the rest are ostrich feathers.

The prices of the feathers per kg are:

FeatherPrice35</text><textx="288"y="351"dominantbaseline="alphabetic"fontfamily="geogebrasansserif,sansserif"fontsize="48"textdecoration="normal">95</text><text x="288" y="351" dominant-baseline="alphabetic" font-family="geogebra-sans-serif, sans-serif" font-size="48" text-decoration="normal">9572$PigeonGooseOstrich

What is the price per kg of the mix?

2

Step-by-step solution

To solve this problem, we'll calculate the weighted average price per kilogram of the feather mix:

  • First, determine the percentage of ostrich feathers. Since pigeon and goose feathers add up to 74%, ostrich feathers comprise 26% of the mix.
  • Next, convert the percentages to decimals:
    • Pigeon feathers: 42%=0.42 42\% = 0.42
    • Goose feathers: 32%=0.32 32\% = 0.32
    • Ostrich feathers: 26%=0.26 26\% = 0.26
  • Now, apply the weighted average formula: Weighted Average Price=(35×0.42)+(95×0.32)+(72×0.26) \text{Weighted Average Price} = (35 \times 0.42) + (95 \times 0.32) + (72 \times 0.26) Calculating these:
    • Pigeon contribution: 14.7 14.7
    • Goose contribution: 30.4 30.4
    • Ostrich contribution: 18.72 18.72
  • Summing these contributions gives us the total weighted average price: 14.7+30.4+18.72=63.82 14.7 + 30.4 + 18.72 = 63.82

Therefore, the price per kilogram of the feather mix is \63.82\).

3

Final Answer

\( 63.82

Key Points to Remember

Essential concepts to master this topic
  • Rule: Find missing percentage by subtracting known percentages from 100%
  • Technique: Convert percentages to decimals: 42% becomes 0.42 in calculations
  • Check: All percentages sum to 100% and weighted contributions total correctly ✓

Common Mistakes

Avoid these frequent errors
  • Using percentages instead of decimals in calculations
    Don't multiply prices by percentages like 42 directly = inflated results! This gives answers 100 times larger than correct values. Always convert percentages to decimals first: 42% becomes 0.42.

Practice Quiz

Test your knowledge with interactive questions

Norbert buys some new clothes.

When he gets home, he decides to work out how much each outfit cost him on average.

PriceOutfit4 T-shirts2 pairs of shorts3 pairs of pants2 sweaters45$50$80$100$210$1 coat

What answer should he come up with?

FAQ

Everything you need to know about this question

Why do I need to convert percentages to decimals?

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Percentages are actually fractions out of 100! When calculating, 42% means 42/100 = 0.42. Using 42 instead of 0.42 gives you an answer that's 100 times too big.

How do I find the missing percentage?

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Since all percentages must add up to 100%, subtract the known ones: 100% - 42% - 32% = 26% ostrich feathers. Always check that your percentages total 100%!

What is a weighted average?

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A weighted average gives more importance to items that make up larger portions of the mix. Each price is multiplied by its percentage, then all products are added together.

Can I solve this problem differently?

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Yes! You could imagine 100 kg of mix: 42 kg pigeon, 32 kg goose, 26 kg ostrich. Then calculate: (42×35)+(32×35) + (32×95) + (26×72)=72) = 6,382 for 100 kg = $63.82 per kg.

How do I check if my weighted average is reasonable?

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Your answer should be between the lowest and highest individual prices. Since prices range from 35to35 to 95, an answer of $63.82 makes sense!

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