Quality control with defective rate: A crate has 1 bruised apple for every 40 apples. If 3 out of every 4 bruised apples are unsaleable and there are 9 unsaleable apples, how many apples are in the crate?

Introduction / Context:
This problem combines ratio interpretation with fractional filtering of defects. We are told the frequency of bruised apples and the fraction of bruised apples considered unsaleable. From the number of unsaleable apples, we back-calculate the total count.

Given Data / Assumptions:

• Bruised frequency: 1 bruised per 40 apples
• Unsaleable among bruised: 3/4
• Unsaleable apples = 9

Concept / Approach:
Let total apples be N. Then bruised apples = N/40. Unsaleable apples = (3/4) * (N/40) = 3N/160. Set 3N/160 = 9 and solve for N.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 500/390/632: None satisfy 3N/160 = 9; they give non-integer or wrong unsaleable counts.

Common Pitfalls:

• Using 1/4 instead of 3/4 of bruised apples as unsaleable.
• Forgetting that 1 bruised per 40 apples means bruised = N/40, not N*40.

Final Answer: