At the Megalopolis Zoo they make a special feed to provide to their exotic birds. It is (by mass) 1/3 super meal, 1/8 commercial birdseed, and one-eighth cracked corn. The rest is made up of Nutro Feedofill. How much commercial birdseed is required to make 97 kilograms of the special feed? If the answer is not a whole number, express your answer as a fraction.
First, we need to figure out what fraction of the feed is made up of commercial birdseed. We can combine the super meal, commercial birdseed, and cracked corn and find that they make up $\frac{1}{3}+\frac{1}{8}+\frac{1}{8}=\frac{11}{24}$ of the feed. This means that the Nutro Feedofill makes up $\frac{13}{24}$ of the feed.
To find out how much commercial birdseed is needed for 97 kg of the feed, we can set up a proportion:
$$\frac{1}{8}\cdot x=\frac{11}{24}\cdot 97$$
Simplifying the right side, we get:
$$\frac{11}{24}\cdot 97=\frac{1057}{24}$$
Multiplying both sides by 8, we get:
$$x=\frac{1057}{3}$$
Since this is not a whole number, our final answer is $\boxed{\frac{1057}{3}}$ kilograms of commercial birdseed.
To find out how much commercial birdseed is required to make 97 kilograms of the special feed, we need to calculate the fraction of commercial birdseed in the mixture.
According to the given information, the special feed consists of:
- 1/3 super meal
- 1/8 commercial birdseed
- 1/8 cracked corn
- The rest is Nutro Feedofill
To calculate the fraction of commercial birdseed, we need to add up the fractions of all the ingredients and subtract them from 1 (since the remaining portion is Nutro Feedofill).
Fraction of commercial birdseed = 1/8
Now, we can find the amount of commercial birdseed required to make 97 kilograms of the special feed:
Amount of commercial birdseed = (Fraction of commercial birdseed) * (Total mass of the special feed)
Amount of commercial birdseed = (1/8) * 97
To simplify this fraction multiplication, we can multiply the numerator (1) by 97 to get the final result:
Amount of commercial birdseed = (1 * 97) / 8
We can simplify this further:
Amount of commercial birdseed = 97/8
Therefore, to make 97 kilograms of the special feed, we require 97/8 kilograms of commercial birdseed.