- If the girls stop when they have written the same number of invitations, what time will it be?
- Together, how many invitations will they have written?
- Each invitation is for two people. Two-thirds of the people who receive invitations attend the party. Remembering that Alice and Jessica do not get invitations but are the hostesses, and Grandmother does not receive an invitation because she is the guest of honor, how many people are at the party?
You could have made a table with the time and the number of invitations each girl made per hour. By 10:00, Alice will have done 20 invitations. At 11:00, 30 and 15 invitations will be produced by Alice and Jessica respectively. At 12:00, Alice would have completed 40 and Jessica would have done 30. At 1:00, 50 and 45 will be done. At 2:00, they will have both done 60 invitations for a total of 120 invitations. 2/3rds of the people invited would be 160 people in attendance. But don’t forget you need include Alice, Jessica and their Grandmother so there would be a total of 163 people at the party.
Ms. L.
16 comments:
SK
8:00 am
10 0
20 0
30 15
40 30
50 45
60 60
The two girls were writing invitations. One could make 10 an hour. The other could make 15. The second one started at 10. The first started at eight. If they stopped when they both had the same amount they would stop at 1:00 pm. At this point, they would have 120 invitations all together. If the invitations were for two people each and 2/3 of the invited arrived, there would be 163 people at the party.
I figured out the first question by creating a table starting at 8:00, and kept going, with Jessica starting 2 hours late, it ended up ending at 1:00 pm. The second question was simple. I just doubled the number 60 which was where they stopped with the same number. This equaled 120. The third question was a bit trickier. I doubled the number 120 because each invitation was for 2 people. Then, since only 2/3s of the invited arrive, I divided 240 by three, which equaled 80, after doubling 80 for 2/3s I had 160. After adding the kids and grandma, my answer was 163.
J.M.
1. It would take Alice 6 hours if she started at 8:00 a.m. and made 10 invitations an hour for 6 hours. She made 60 invitations, and ended at 2:00 p.m. Jessica started at 10:00 a.m. She made 15 invitations an hour. She also ended at 2:00 p.m. and also made 60 invitations.
Time Invitations Time Invitations
Alice Jessica
8:00 0 10:00 0
9:00 10 11:00 15
10:00 20 12:00 30
11:00 30 1:00 45
12:00 40 2:00 60
1:00 50
2:00 60
2. Together Alice and Jessica made 120 invitations.
3. 80 people showed up at the party.
ZB
1. At 2:00 pm, both girls would have written 60 invitations. I figured this out by finding the common multiple of 10 and 15.
2. Together both girls made 120 invitations. I figured this out by adding the 60 invitations they made together.
3. 160 people attended the party. Since 120 invitations were made, and each invitation was made for two people, 240 people were invited. Two-thirds of that would be 160 people.
AM RT
1. The time would be 2 o clock because Alice started at 8 o clock and she writes 10 invites an hour and for her to get 60 invitations it takes her 6 hours to get to 60 invites and it would be 2 o clock. Jessica started at 10 am and writes 15 invites per hour and for her to get to 60 invites it takes her 4 hours to get to 60 invites witch is 2 o clock.
2. They would have written 120 invites because Alice made 60 invites and so did Jessica. If you add 60 plus 60 it would be 120 invites.
3. The amount of people that showed up is 158 because 120 plus 120 is 240 and two thirds is 160 and Alice and Jessica don’t need one because they are the hostesses and grandma doesn’t need one because it’s her birthday.
E.R.
1. At 2:00pm, each girl would have written 60 invitations. I figured this out because 60 is the lowest common multiple that matches up.
2. Together, both of girls made 120 invitations. I figured this out by adding the 60 invitations they each made together.
3. I think 160 people came to the party. Since 120 invites were made and each one was for two people, 240 were invited. Two-thirds of that is 160.
M.M.
When the girls had written the same number of invitations it would be 1:00. It would be 1:00 because Jessica started at 10:00 A.M and works for four hours, and Alice starts at 8:00 A.M and works for six hours, 117 people attended the party because yes, two-thirds of people with which would be 1:00 each. Therefore the made 60 invitations. 117ple invitations attended the party, but some people might have attended the party with out invites. Such as really close friends might haven’t gotten an invite and just a call.
Table to salve number 1:
Started at 10:00, made 15 per hour. Jessica: 1 hour, 15. 2 hours 30. 3 hours 45. 4 hours 60.
Started at 8:00 made 10 per hour. Alice: 1 hour, 10. 2 hours 20. 3 hours, 30. 4 hours, 40. 5 hours, 50. 6 hours, 60.
WO AND JD 8.20.2009
10 0
20 0
30 15
40 30
50 45
60 60
Alice Jessica
8:00
1:00
When the girls stop when they have the same number of invitations, it will be 1:00. The reason I know this is because Alice started before Jessica so on the table you must start Alice’s data before Jessica. When the numbers came out to be the same, the time was one o’clock.
Together the girls have written 120 invitations. I know this because when the same numbers came together, at the number at 60. Since that is the number they both stopped at, you have to double the number which comes out to 120.
The answer for this question is 43. The way I got the answer to this question is: first I divided 120 by two because every invitation is for two people. Then I divided 60 by three because two-thirds of the people who received an invitation attended the party. Then if you add the guest of honor and the two girls, the answer is 43.
MJS
1. This is my answer: Alice started at 8:00am and made 10 invitations an hour and Jessica started at 10:00am and made 15 invitations an hour. Jessica would be 5 invitations short of Al
Time Invitation Time Invitation
8:oo O 10:00 0
9:00 10 11:00 1
10:00 20 12:00 30
11:00 30 1:00 45
12:00 40 2:00 60
1:00 50 3:00 75
2:00 60 4:00 90
2. All together they make 150 invitations
3. Two thirds of the invitations is 50
A.W.
If you started Alice and Jessica at 10:00 a.m. it would be easier to find the answer. I just kept going until I found the answer. So at 1:00 p.m. they would have the same amount of invitations made. Also, they would have 60 invitations altogether if they stopped at 1:00 p.m. If only two-thirds of the people came, of the 60 invitations, and each is for two people you will have 80 people there.
A.L.
Alice Time Jessica Time
10 8:00 a.m. 8:00 a.m.
20 9:00 a.m. 9:00 a.m.
30 10:00 a.m. Starting time: 15 10:00 a.m.
40 11:00 a.m. 30 11:00 a.m.
50 12:00 p.m. 45 12:00 p.m.
60 1:00 p.m. 60 1:00 p.m.
70 2:00 p.m. 75 2:00 p.m.
80 3:00 p.m. 90 3:00 p.m.
90 4:00 p.m. 105 4:00 p.m.
100 5:00 p.m. 120 5:00 p.m.
110 6:00 p.m. 135 6:00 p.m.
120 7:00 p.m. 150 7:00 p.m.
130 8:00 p.m. 165 8:00 p.m.
Problem #1
I got 60 invitations at 1:00 p.m. when they both at the same number of invitations. I got that answer by using a table and starting them both off at 10:00 a.m. I just kept counting until they were both at the same number of invitations at the same time. For number 2 I got 120 invitations. I got that by adding 60 and 60 together and getting a grand total of 120 invitations. For 3 I got 163 people attended the party. I got that by dividing 60 by 3 for both of them. I got 40. Then I added 40 and 40 together and got 80. Then I had to add Grandma, Alice, and Jessica and that added up to 3 more people. So I added 80 plus 3 and got a grand total of 83.
C.D.
1. At 8:00 Alice starts making invitations, by 10:00 she’s already made 30.
Also at 10:00 Jessica starts making invitations. If they keep making invitations by 1:00 they should have the same amount of invitations.
2. If you put the invitations together there should be 120.
3. Each invitation is for 2 people so 120+120=240 so 240 is how many people were supposed to come. But only 2/3 came 1/3 of 240 is 80. 80+80=160 so 160 people came to the party.
TD AND TM
1. At 2 o’clock each of the girls would have written 60 invitations. We got this answer by seeing what number 15 and 10 would both go into evenly and from that information seeing which time would match up evenly with the numbers.
2. Together they would have written 120 invitations. We got this answer by seeing which number 10 and 15 go into evenly and seeing which time they both made the same amount of invitation.
3. 158 people will be at the party. We found this out by using the information that each invitation is for two people and 120 multiplied by two is 240 and only two thirds of the people attend so two thirds of 240 is 160 and Alice and Jessica didn’t need an invitation since they were the hostesses and their grandma was the guest of honor so neither of them needed an invitation and one invitation was for two people so Alice, Jessica, and their grandmother would only need two invitations. Therefore the answer must be 158.
MF MW
1. It 2:00 p.m., the girls will each have 60 invitations. This is because Alice made 10 invitations an hour and started at 8 a.m., which would mean at 2 p.m. 6 hours would have passed and she would’ve had 60 invitations finished( 6 multiplied by 10 is 60). Jessica started at 10 a.m. and made 15 invitations an hour so at 2 p.m. 4 hours would have passed and she would have 60 invitations just like Alice ( 15 multiplied by 4 is 60).
2. Together, they would have written 120 invitations. This is because Alice and Jessica each wrote 60 invitations. 60 + 60 = 120.
3. At the party, there would be 160 people. This is because 120 invitations were made, and 1invetation is for 2 people. 240 people are invited and two thirds of that is 160.
E.A.W.
1.Alice did 10 invites an hour, while Jessica did 15 invites an hour. They started at separate times. At one o'clock they ended at 60 invites each.
2. Together they will have written 120 invitations. I know this because at 1:00 60 + 60 = 120.
3. Because each invitation is for two people, I multiply the total number of invites (120) to get 240 people. When you split 240 into thirds, you get 80 + 80 + 80. Because only two-thirds came you only add 80 + 80, which equals 160. Then you have to add the two girls (the hostesses) and the grandma. So, 160 + 3 = 163. 163 people attended.
MG
1. If the girls stop at the same time when they have written the same number of invitations it will be 1:00pm. (They will also have made 60 invitations)
2. Together, they will have made 120 invitations. I figured that out by adding the number of invitations they have made when they stop at the same time. The answer to the first question was 60, so 60 +60=120.
3. The amount of people would be163. I got that answer by adding 120+ 120=240. 240 divided into thirds are 80. Two-thirds of the party showed up which would be 160, and then you add the grandmother, Alice, and Jessica and you have 163 all together.
AR
Time 8:00 9:00 10:00 11:00 12:00 1:00 2:00
Alice 0 10 20 30 40 50 60
Jessica 0 0 0 15 30 45 60
Alice and Jessica will have made the same amount of invitations at 2:00 pm. I made the table above to solve the problem. Alice starts at 8:00 but she doesn’t have any made at 8:00, she has them made at 9:00. It’s the same with Jessica, she starts at 10:00 but doesn’t have any made until 11:00. They have 120 invitations all together because 60 plus 60 equals 120. A total of 163 will attend the party because there are two people for each invitation so that would make 240 people, but only two-thirds attend the party. Two-thirds of 240 equals 160 plus the grandma, Alice, and Jessica is 163.
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