To solve the problem, you need to determine the amount of waste produced when making applesauce.
The problem states that for every 9 parts of applesauce, 2 parts are waste (cores). You're also given that the production yields 24.5 parts of applesauce.
First, find the total parts (applesauce + waste):
Given the ratio:
- 9 parts applesauce : 2 parts waste
This means for every 11 parts in total, 9 are applesauce and 2 are waste.
Now, to find the amount of waste produced when having 24.5 parts of applesauce, set up the proportion:
[
\frac{9}{11} = \frac{24.5}{x}
]
Where ( x ) is the total amount of parts (applesauce + waste).
Solving for ( x ):
[
x = \frac{24.5 \times 11}{9} = 29.9444
]
Now, find the amount of waste:
Since the ratio of waste in the total parts is 2 parts of waste for every 11 parts total, calculate:
[
\text{Waste} = \frac{2}{11} \times 29.9444
]
Solve for the waste:
[
\text{Waste} \approx 5.444
]
So, about 5.44 parts are waste.
