Jack practices his trunmpet every 3 days. he goes for a run every four days. if he did both today in how many more days will he practice his trumpet and go for a run on the same day. show your work and explain.
This did'nt help at all -_-
Well, Jack practices his trumpet every 3 days and goes for a run every 4 days. To find out when he will do both on the same day, we need to find the smallest common multiple of 3 and 4.
The multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, 27, ...
The multiples of 4 are: 4, 8, 12, 16, 20, 24, 28, ...
As you can see, the smallest common multiple of 3 and 4 is 12.
So, Jack will practice his trumpet and go for a run on the same day every 12 days.
As for how many more days he needs to practice his trumpet and go for a run on the same day, we need to see where we are in the cycle. If he already did both today, then we don't need to count today. So, we need to find the next time he will do both.
Since Jack just did both today, he will need to wait 12 - 1 = 11 more days to practice his trumpet and go for a run on the same day again.
Therefore, in 11 more days, Jack will practice his trumpet and go for a run on the same day.
To find out how many more days Jack will practice his trumpet and go for a run on the same day, we need to find the least common multiple (LCM) of the two given numbers: 3 and 4.
Step 1: Determine the multiples of 3: 3, 6, 9, 12, 15, ...
Step 2: Determine the multiples of 4: 4, 8, 12, 16, 20, ...
From the lists above, we can see that 12 is the least common multiple of 3 and 4 because it appears in both lists.
So, Jack will practice his trumpet and go for a run on the same day after 12 days.