Question

Mr. Gifford wishes to put 372 eggs into cartons that can hold 12 eggs each. If he has 50 empty cartons and completely fills as many of them as possible with the 327 eggs, how many of the cartons will remain empty?

• A. 12
• B. 15
• C. 19
• D. 28
• E. 31

Hint:

In word problems, always watch out for extraneous information or possible typos. If your initial calculation leads to an answer that isn't an option, re-read the problem carefully and see if another interpretation of the numbers makes sense and matches an answer choice.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This is a word problem that requires careful reading to identify the correct numbers to use for the calculation. The problem involves division to determine how many cartons are used and then subtraction to find out how many are left empty. There appears to be a typo in the question, as two different numbers of eggs (372 and 327) are mentioned. Using 372 eggs leads to one of the answer choices, while using 327 does not. We will proceed assuming 372 is the correct number of eggs.
Step 2: Key Formula or Approach:
1. Calculate the number of cartons filled by dividing the total number of eggs by the number of eggs per carton.
2. Calculate the number of remaining empty cartons by subtracting the number of filled cartons from the total number of available cartons.
Step 3: Detailed Explanation:
Let's assume the total number of eggs to be packed is 372.
The capacity of each carton is 12 eggs.
First, we find the number of cartons that can be completely filled:
\[ \text{Number of cartons filled} = \frac{\text{Total eggs}}{\text{Eggs per carton}} = \frac{372}{12} \] \[ \frac{372}{12} = 31 \] So, 31 cartons are completely filled.
Next, we find how many cartons remain empty.
Total number of available cartons = 50.
Number of cartons used = 31.
\[ \text{Number of empty cartons} = \text{Total cartons} - \text{Cartons filled} \] \[ \text{Number of empty cartons} = 50 - 31 = 19 \] 19 cartons will remain empty. This matches option (C).
(Note: If we were to use the number 327, the number of filled cartons would be \(\lfloor \frac{327}{12} \rfloor = \lfloor 27.25 \rfloor = 27\). The number of empty cartons would be \(50 - 27 = 23\), which is not among the options.)
Step 4: Final Answer:
Based on the calculation using 372 eggs, 19 cartons will remain empty.