If teacher x gives a pop quiz on Monday and then every five classes, and teacher y gives a pop quiz on Monday and then every six days, how many school days will it be until both give quizzes on the same school day
days for test x are multiples of 5
days for test y are multiples of 6
what smallest number would be divisible by both 5 and 6 ?
To find the number of school days until both teachers give quizzes on the same day, we need to determine the least common multiple (LCM) of the two intervals.
Teacher x gives a quiz every 5 classes, which means there will be a quiz on day 5, 10, 15, and so on.
Teacher y gives a quiz every 6 days, which means there will be a quiz on day 6, 12, 18, and so on.
To find the LCM of 5 and 6, we can list the multiples of each number until we find a common multiple:
Multiples of 5: 5, 10, 15, 20, 25, 30, 35...
Multiples of 6: 6, 12, 18, 24, 30, 36, 42...
From the lists, we can see that 30 is the smallest number that is a multiple of both 5 and 6. Therefore, it will take 30 school days for both teachers to give quizzes on the same day.
So the answer is 30 school days.