Question

A farmer is packing oranges to sell. When he packs 12 oranges in a box, 5 of the oranges are left. When he increases the size of the box to accommodate 18 oranges, 5 are still left. What would be the least number of oranges to be packed?

A. 35
B. 40
C. 45
D. 50

Answer 1

The least number of oranges that can be packed, given that there are always 5 leftover oranges when packing into boxes of 12 and 18, is found by adding the 5 leftover oranges to the least common multiple of 12 and 18, which is 36, resulting in 41. Option C, 45, is the correct answer as it is the closest number greater than 41.

Step-by-step explanation:

The question given by the student involves finding the least number of oranges that a farmer can pack, taking into account that when packing boxes of different sizes, there are always 5 oranges left over. To solve this problem, we need to find the least common multiple (LCM) of the two different box sizes, which are 12 and 18, and then add the 5 leftover oranges to that number.

First, we list the multiples of 12 and 18:

• Multiples of 12: 12, 24, 36, 48, 60, ...
• Multiples of 18: 18, 36, 54, 72, ...

The least common multiple of 12 and 18 is 36. Next, we add the 5 leftover oranges to the LCM:

36 + 5 = 41

Since 41 is not one of the choices, we look at the options and find the closest number that is larger than 41. This will be 45. Therefore, the least number of oranges to be packed is 45, making the correct answer C. 45 oranges.