Question

In the beast school, english homework assignments are due every 9 days, math homework assignments are due every 12 days, and science homework assignments are due every 15 days. if all three homework assignments were due together today, how many times in the next 300 days will exactly two homework assignments be due together (including the 300th day)?

Answer 1

To find the number of times exactly two homework assignments will be due together in the next 300 days, we need to find the least common multiple (LCM) of the periods at which each assignment is due. The LCM of 9, 12, and 15 is 180. This means that every 180 days, exactly two assignments will be due together. Dividing 300 by 180 gives us a quotient of 1 and a remainder of 120. This means that two assignments will be due together once in the next 300 days and an additional two assignments will be due together in the remaining 120 days. Therefore, in the next 300 days, exactly two homework assignments will be due together 3 times.

Step-by-step explanation:

To find the number of times exactly two homework assignments will be due together in the next 300 days, we need to find the least common multiple (LCM) of the periods at which each assignment is due.

The LCM of 9, 12, and 15 is 180. This means that every 180 days, exactly two assignments will be due together.

Dividing 300 by 180 gives us a quotient of 1 and a remainder of 120. This means that two assignments will be due together once in the next 300 days and an additional two assignments will be due together in the remaining 120 days.

Therefore, in the next 300 days, exactly two homework assignments will be due together 3 times.