Its a word problem and I have a hard time understanding word problems. Patsy has cheerleading practice on every fourth school day. She wants to be in the school play, but they have practice on every sixth school day. If both started on September 5th what would be the first date that she has to choose between cheerleading and play practice? I know that on the 23d of Sept. she will have to choose one but I don't know how to figure it out beside looking at a calendar.
Find the least common multiple of 4 and 6.
is it not 2 the least common multiple of 4 and 6?
no, 2 is the greatest common divisor.
LCM is 12 because
4 = 2*2
6 = 2*3
The smallest multiple must contain 2*2*3 = 12
oh ok thank you.
oh ok thank you. So what day did you come up with Steve?
I just don't understand how to find out the day she has to chose one or the other? I am so lost?
Please read again what Steve posted:
"12 days is 2 weeks + 2 days.
If she starts on Mon-Wed, then 12 school days is two calendar weeks + 2 days:
5+7+7+2 = 21
So, the 5th must be a Thu or Fri, giving us the extra 2 days for the weekend. "
To solve this word problem, we can use the concept of finding the least common multiple (LCM) of two numbers. In this case, we want to find the first date when Patsy has to choose between cheerleading and play practice.
Let's break it down step by step:
1. Calculate the LCM of 4 and 6:
- The multiples of 4 are: 4, 8, 12, 16, 20, 24, ...
- The multiples of 6 are: 6, 12, 18, 24, ...
As we can see, the first common multiple of 4 and 6 is 12. Therefore, the LCM of 4 and 6 is 12.
2. Determine the number of days from September 5th until the first common multiple:
- September 5th counts as the first school day.
- To find the first date, we need to add multiples of both 4 and 6. Starting from September 5th, we count:
- September 5th (1st day)
- September 6th (2nd day)
- September 7th (3rd day)
- September 8th (4th day) --> first cheerleading practice
- September 9th (5th day)
- September 10th (6th day) --> first play practice
Now, we have reached the first common multiple (12th day).
3. Determine the date of the first common multiple:
- We started on September 5th, so we count 12 days from that date.
- September 5th + 12 days = September 17th.
Therefore, the first date when Patsy has to choose between cheerleading and play practice is September 17th.
you need to find the smallest number which is a multiple of both 4 and 6. That is 12. Since we're talking school days, we only count Mon-Fri.
So, 12 days is 2 weeks + 2 days.
If she starts on Mon-Wed, then 12 school days is two calendar weeks + 2 days:
5+7+7+2 = 21
So, the 5th must be a Thu or Fri, giving us the extra 2 days for the weekend.