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

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:

$</text><text x="288" y="351" dominant-baseline="alphabetic" font-family="geogebra-sans-serif, sans-serif" font-size="48" text-decoration="normal">95$72$PigeonGooseOstrich

What is the price per kg of the mix?

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: $42\% = 0.42$
  • Goose feathers: $32\% = 0.32$
  • Ostrich feathers: $26\% = 0.26$
• Now, apply the weighted average formula: $\text{Weighted Average Price} = (35 \times 0.42) + (95 \times 0.32) + (72 \times 0.26)$ Calculating these:
  • Pigeon contribution: $14.7$
  • Goose contribution: $30.4$
  • Ostrich contribution: $18.72$
• Summing these contributions gives us the total weighted average price: $14.7 + 30.4 + 18.72 = 63.82$

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