Lora's gymnastics class practices floor exercises every other day. The class practices on the balance beam every third day, the uneven bars every fourth day. Today is March 10, and the class practiced all 3 events.How many more times, before June 1, will the class practice all 3 on the same day?
Jhed/May -- I think you can figure this out the same way I showed you for your last post.
To find out how many more times the class will practice all three events on the same day before June 1, we need to determine the pattern of when each event aligns.
We know that the gymnastics class practices floor exercises every other day, so they will practice it on March 10, 12, 14, etc.
The class practices on the balance beam every third day, so they will practice it on March 10, 13, 16, etc.
The class practices on the uneven bars every fourth day, so they will practice it on March 10, 14, 18, etc.
We need to find the least common multiple (LCM) of 2, 3, and 4 to determine when they will align again.
Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20...
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24...
Multiples of 4: 4, 8, 12, 16, 20...
From the above lists, we can see that the LCM of 2, 3, and 4 is 12.
This means that on the 12th day, the gymnastics class will practice all three events on the same day. Since they already practiced all three events on March 10, we need to count the number of times they will practice all three again before June 1.
From March 10 to June 1, there are 83 days.
To calculate the number of times they will practice all three, we divide 83 by 12 (the LCM) and ignore any remainders:
83 ÷ 12 = 6 R 11
Therefore, they will practice all three events on the same day an additional 6 times before June 1.
Note: I assumed that the class will continue practicing the same pattern without any deviations or changes.