Emilio’s family volunteers at the local soup kitchen every 30 days. Emilio has swimming
lessons every 9 days. He has both activities
this Saturday. When will he have both
activities again on the same day?

Emilio will have both activities again on the same day after 90 days from this Saturday.

Step-by-step explanation:

To solve this question list the multiples of 30 and 9 to find the first common multiple because the two activities will happen again in a number divisible by both 30 and 9.

∵ The multiples of 30 are: 30, 60, 90, 120,

∵ The multiples of 9 are: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99,

→ The common multiple is 90

∴ The common multiple of 30 and 9 is 90

→ That means the activities will meet again after 90 days from

   this Saturday

Emilio will have both activities again on the same day after 90 days from this Saturday.