Building Bouquets
Mrs. Warren owns and operates an independent flower shop. To help sell more flowers (and cut down on waste), she offers a daily special of bouquets or corsages created from "leftovers" from larger orders.
With today's batch of leftovers, Mrs. Warren decides to try 4 flowers in each bouquet, but she has three extra flowers left. To make pricing easier, she wants the specials to be the same size, so she tries making the bouquets with 7 flowers each... but then there are two flowers left. If she makes bundles of 8 flowers, she has three flowers left.
- What is the smallest possible number of flowers that Mrs. Warren has to work with?
- With the number of flowers determined above, how many bouquets or corsages and of what size can Mrs. Warren make?
Extra: Do you think that Mrs. Warren would ever have enough leftovers that it wouldn't matter if she chose to make bouquets of 7, 8, or 9 flowers? (Don't forget - Mrs. Warren doesn't want to waste a single flower.)
CI
ReplyDeleteOctober, 15th 2010
6th grade honors
4 in each
3 extra
7 each
2 extra
8 in each
3 extra
1. 2? Because, 2 is an even number and I believe since there were 3 extra, she would only have 1 extra. Well, she would have one extra. So obviously, it would come out un-even. This problem also is incomplete. It never does tell you how many left-over flowers there are in the pile.
2. Well I couldn’t determine it.
H M
ReplyDelete1. 9 is the smallest number that Mrs. Warren can work with.
2. She can make 10 bouquets and 4 flowers in each
dsb
ReplyDeleteI think that 2 is the lowest
I think that 2 flour bouquets with 2 flours
October 15, 2010
ReplyDeleteL.Y.
My answer to October 15th question
4+4 8
8+3 11
So then there are 11 flowers and 11 is an odd number and nothing goes into it evenly but it’s self… she can try 3 flowers in each bouquet and there would only be 2 left but if you did 2 in each bouquet then there would be 1 left over and you could have 5 bouquets in total.
1. The lowest number of flowers in each bouquet is 2, with only 1 flower left over.
2. The amount of bouquets she can have with having 2 flowers in each bouquet is 5 bouquets.
m.h.
ReplyDeleteAnswer: 1. I made a table of a lot of the multiples of 4,7, and 8. When they tried to use 4’s, they had 3 left over, so I knew that the answer had to be a number 3 counts after a multiple of 4. So I went through all the numbers that were 3 counts after a multiple of 4 and looked to see if it would match with the other two numbers. Once I got to the number 51, I found out that it matched all three fractions. Because, 4 goes into 48 and 48 plus 3 would be 51, so I knew it worked for 4. Then I went to 8 and saw that it went in to 48 and 48 plus 3 is 51, so I knew it worked for 8. Then I saw that 7 went into 49, and 49 plus 2 is 51, so 7 worked too. So the answer to the first question is 51.
2. I found the factors of 51 and all I could come up with was 17 and 3, 3 and 17, 1 and 51, and 51 and1. So they could do 1 bouquet of 51 flowers, 51 bouquets of 1 flower, 3 bouquets of 17 flowers, or 17 bouquets of 3 flowers.
JM ANSWER:1.The smallest number of flowers she has to work with is 56.First I found the LCM of 4, 7, and 8 witch equaled 56.
ReplyDelete2.Ms.Warren can make 7 bouquets of 8, 8 bouquets of 7, and 4 bouquets of 14.
Extra. I think she would not have enough because 9 does not go into 56 evenly.
REDO
ReplyDeleteOctober 15th 10
L.Y.
My answer to October 15th question
4+4 8
8+3 11
So then there are 11 flowers and 11 is an odd number and nothing goes into it evenly but it’s self… she can try 3 flowers in each bouquet and there would only be 2 left but if you did 2 in each bouquet then there would be 1 left over and you could have
5 bouquets.
1. The lowest number of flowers in each bouquet is 2, with only 1 flower left over.
2. The amount of bouquets she can have with having 2 flowers in each bouquet is 5 bouquets.
What Mrs. Warren can do with the leftover flower is to throw it away.(since it’s already a leftover before it became once again…)
ZH:
ReplyDelete1. The smallest number of flowers she has to work with is 56
I found the LCM of 4, 7, and 8.This was 56.
2. Ms. Warren could make 4 bouquets of 14, 7 bouquets of 8, and 8 bouquets of 7
FA answer: The smallest amount of flowers is 56. I found the LCM between the given numbers of numbers 4, 7, 8.
ReplyDelete1.8/2=4/2=2= 23 7/1=7 4/2=2=22
LCM= (23) (7)
(8) (7)
56
2. Ms. Warren could make 4 bouquets of 14, 7 bouquets of 8, and 8 bouquets of 7. These are the ways she can do it.
TL answer: the smallest amount of flowers is 56. The LCM that I found by using the numbers 4, 7, 8.
ReplyDelete4 -(22) 7-(7)(1) 8-(23)
LCM= (23)(7)
(8) (7)
56
1. The bouquet of 4 flowers. 4-3is 1 7-2 is 5 8-3 is 5
ReplyDelete2. She can make 4 bouquets with the extras and the bouquets she already made.
*EXTRA: Yes, you would just have use the LCM. It could be 504
7 8 9
7 4 2 3 3
(7) 2 2
(23) (32)
LCM: (23) (32) (7)
(8) (9) (72)
(72)(7) (504)
1.The smallest possible number that Ms. Warren has to work with is 224.
ReplyDelete2.With the number of flowers determined above, Ms. Warren can make 124 corsages or bouquets.
Extra: I think that Ms. Warren would ever have enough leftovers that it wouldn’t matter if she chose to make bouquets of 7, 8, or 9 flowers.
B.V
RB
ReplyDeleteI tried to find a number that left 3 extra if it was divided by 8 and 4, and 2 extra if it was divided by 7. Here’s what I did:
75= If you knock off three, it’s divisible by 4 and 8, which is one of the things I’m looking for. But, if you take off two, it’s not divisible by 7. So the number 75 has nothing to do with the answer.
51= If you remove two from the total, it gives you 49, which is divisible by 7. I f you remove three, you are left with 48 which is divisible by 4 (12 times) and 8 (6 times).
Now, I know that 51 is my total because it was noted in paragraph 2 in the problem that the number had to be divisible by 4 and 8 leaving 3 left, and 7 leaving 2 left. So, 51 is the smallest possible number that Mrs. Warren has to work with.
Mrs. Warren needs to know how many bouquets and what size she can make without leaving a lot of extra flowers. She can’t have huge bouquets because she wants to keep the price of the bouquet down.
Possible combinations:
5 flowers per bouquet, 10 bouquets, 1 extra flower
10 flowers per bouquet, 5 bouquets, 1 extra flower
*51 is a prime number, so there will always be at least 1 flower extra
So, the best answer is 5 flowers per bouquet.
-It won’t be too expensive because there are only 5 flowers
-There is very little waste, i.e. only 1 flower
-There are 10 bouquets you can make, which is a lot
T.M.
ReplyDeleteFirst I found the lowest common multiple of 7, 8 and 4. That is 56. So that is how many flowers she has to work with. Ms.Warren can make a bouquet with 7 or 8 flowers because 7 and 8 both go into 56.
1: The smallest number possible Mrs. Warren can work with is 162
ReplyDelete2: she should use 4 so you can use a small amount but still make a lot of bouquets.
S (A) M
1. The smallest possible number that Ms. Warren has to work with is 224 because 4 times 7 times 8 equal 224.
ReplyDelete2. With the number of flowers determined above, Ms. Warren can make 124 corsages or bouquets because 224 divided by eight, four, and 7 plus the extras, equal 124 added together.
Extra: I think that Ms. Warren would ever have enough leftovers that it wouldn’t matter if she chose to make bouquets of 7, 8, or 9 flowers.
B.V
DS I tried to multiply all the numbers together and I got 4608. Then I divided it by 6 because that was how many numbers. That didn’t work so I tried to add all of the numbers that she tried and I got 19. Ms.Warren can make 1 small one with four in it she can make two large ones with seven and one with eight.
ReplyDeleteEK
ReplyDelete1. The smallest possible number of flowers that Mrs. Warren has to work with is 11 flowers
2. she could have 2 4 flower thing and 1 3 flower thing.
extra: it depends on how much business she gets but yes
MG
ReplyDeletePeriod 3
10/23/10
The smallest number of flowers that Ms.Warren has to work with is 2. She can make is 5. bouquets of small size. I added up all the total leftovers. The total leftover was 20. So, I divided 20 by 2 because if I divided it by 4, there would be 3 leftover flowers. 20 divided by 2 is 10. Then, I divided 10 by 2 and got 5. So the lowest number of flowers is 5 per bouquet.
(M.M.)
ReplyDelete1)51/4=12(R3)
51/7=7(R2)
51/8=6(R3)
The smallest possible number of flowers can be 51.
2)51/3=17
(17)(3)=51
Mrs. Warren could have either 3 bouquets of 17 or 17 bouquets of 3 flowers. I got my answer by dividing 51 by 3 and I got the answer 17. (I checked by multiplying 3 by 17)
EXTRA:
7,8,9
LCM- 504
Yes it is possible because if she has 504 flowers, the least common multiple, all three numbers, 7, 8, and 9, go into 504.
LHernandez
ReplyDeleteTHURSDAY, OCTOBER 14, 2010
October 15th
Building Bouquets
Mrs. Warren owns and operates an independent flower shop. To help sell more flowers (and cut down on waste), she offers a daily special of bouquets or corsages created from "leftovers" from larger orders.
With today's batch of leftovers, Mrs. Warren decides to try 4 flowers in each bouquet, but she has three extra flowers left. To make pricing easier, she wants the specials to be the same size, so she tries making the bouquets with 7 flowers each... but then there are two flowers left. If she makes bundles of 8 flowers, she has three flowers left.
1. What is the smallest possible number of flowers that Mrs. Warren has to work with?
2. With the number of flowers determined above, how many bouquets or corsages and of what size can Mrs. Warren make?
Extra: Do you think that Mrs. Warren would ever have enough leftovers that it wouldn't matter if she chose to make bouquets of 7, 8, or 9 flowers? (Don't forget - Mrs. Warren doesn't want to waste a single flower.)
Answer-51 I got this answer by using 7x7=49+2=51 and 6x8=48+3=51 then the last step I did was 4x12=48+3=51 and they all = 51 so that’s how I got my answer.
Extra: I yes but it would depend on how many she wants.
C.I
ReplyDeleteOctober 29th 2010
Problem: Building Bouquets
She has a minimum of three flowers per bouquets. This is so because, when she did a bouquet of 4, she has three leftover. So now she can do 3 in a bouquet, and will only have I believe 1 leftover.
I believe that there could be a possible of a bouquet of one that was 7, one that is 4,one with 2 flowers in it (taking the possible extras from the flowers with 7 in them), and one that had 6 (or two that had 3 because two of the bouquets has three
IDaniel
ReplyDeleteMs. Leckman
3rd Period
Mrs. Warren owns and operates an independent flower shop. To help sell more flowers (and cut down on waste), she offers a daily special of bouquets or corsages created from "leftovers" from larger orders.
With today's batch of leftovers, Mrs. Warren decides to try 4 flowers in each bouquet, but she has three extra flowers left. To make pricing easier, she wants the specials to be the same size, so she tries making the bouquets with 7 flowers each... but then there are two flowers left. If she makes bundles of 8 flowers, she has three flowers left.
1. What is the smallest possible number of flowers that Mrs. Warren has to work with?
2. With the number of flowers determined above, how many bouquets or corsages and of what size can Mrs. Warren make?
Extra: Do you think that Mrs. Warren would ever have enough leftovers that it wouldn't matter if she chose to make bouquets of 7, 8, or 9 flowers? (Don't forget - Mrs. Warren doesn't want to waste a single flower.)
1. Smallest bouquet would include 19 flowers 4-3 is 1 7-2 is 5 8-3 is 5 4+7+8=19
2. 4, 4 flower bouquets. Two, 7 flower bouquets. And two, 8 flower bouquets
1. I found a number where all of the flowers fit in in a way when all of them have the amounts of extra that they do in the situation above. I discovered that the smallest number that meets the criteria is fifty one. Fifty one divided by seven equals seven remainder two, divided by four is twelve remainder three, divided by eight is six remainder three.
ReplyDelete2. Fifty one flowers divided by three equals seventeen, so Mrs. Warren can have seventeen bouquets/corsages of three flowers.
Extra: If Mrs. Warren had five hundred and four flowers, she could make bouquets/corsages of seven, eight, and nine flowers without it mattering how many of each number she did.
C.C.J.
C.C.
ReplyDeleteBuilding Bouquets
Mrs. Warren owns and operates an independent flower shop. To help sell more flowers (and cut down on waste), she offers a daily special of bouquets or corsages created from "leftovers" from larger orders.
With today's batch of leftovers, Mrs. Warren decides to try 4 flowers in each bouquet, but she has three extra flowers left. To make pricing easier, she wants the specials to be the same size, so she tries making the bouquets with 7 flowers each... but then there are two flowers left. If she makes bundles of 8 flowers, she has three flowers left.
1. What is the smallest possible number of flowers that Mrs. Warren has to work with?
2. With the number of flowers determined above, how many bouquets or corsages and of what size can Mrs. Warren make?
Extra: Do you think that Mrs. Warren would ever have enough leftovers that it wouldn't matter if she chose to make bouquets of 7, 8, or 9 flowers? (Don't forget - Mrs. Warren doesn't want to waste a single flower.)
Answers:
1: 4+7+8=19 Flowers
2: Four, 4 flower bouquets. Two, 7 flower bouquets. And 2, 8 flower bouquets.
EXTRA: Yes, if she wants to because if she makes a bouquet of 9 flowers would have one extra flower to add to her bouquet. If she does an 8 flower bouquet she would have three extra flowers and so on.
G.S.:
ReplyDeleteFirst I found the lowest common multiple.
4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56
7: 7, 14, 21, 28, 35, 42, 49, 56
8: 8, 16, 24, 32, 40, 48, 56
I figured there where 56 flowers.
Then to find out the number of boutiques I did this:
56/3=18.66667
I think 18 flowers are in each bouquet. Ms.Warren can make 3 large bouquets.
C.G.
ReplyDeleteFirst I found out the lowest common multiple of eight, seven, and four.
4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56
7: 7, 14, 21, 28, 35, 42, 49, 56
8: 8, 16, 24, 32, 40, 48, 56
I got 56 so there is 56 flowers in all. So I did this…
56 divided by 3 and got 18.666666666667. I divided it by three because there is three numbers. (four, seven, and eight)
There are 18 flowers in each bouquet.
T.M.
ReplyDelete1.First I found the lowest common multiple of 7, 8 and 4. That is 56. So that is how many flowers she has to work with. Ms.Warren can make a bouquet with 7 or 8 flowers because 7 and 8 both go into 56.
4:4,8,12,16,20,24,28,32,36,40,44,48,52,56
7:7, 14,21,28,35,42,49,56
8:8,16,24,32,40,48,56
I got 56 so there are 56 flowers in all. So I divided 56 by 3(because there are three numbers) and got 18.66666667. So there are 18 flowers in each bouquet.
2. First I found the factors of 51 and I came up with 17and 3, 3 and 17, 51and 1, and 1 and 51. So that means Ms.Warren can make 17 bouquets of 3 flowers, 3 bouquets of 17 flowers, 51 bouquets of 1 flower, and 1 bouquet of 51 flowers.
J.T.
ReplyDeleteOCTOBER 15TH
The smallest possible number of flowers that Mrs. Warren can work with is 2 because for each time it gets to 4 or a number that your get when you skip count by 4 there are 3 flower left that why when she uses seven she has two left over so that’s why maybe I thought the smallest number she can work with is two so she wont have left over’s
C.G.
ReplyDeleteFirst I found out the lowest common multiple of eight, seven, and four.
4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56
7: 7, 14, 21, 28, 35, 42, 49, 56
8: 8, 16, 24, 32, 40, 48, 56
I got 56 so there is 56 flowers in all. So I did this…
56 divided by 3 and got 18.666666666667. I divided it by three because there is three numbers. (four, seven, and eight)
So there are 18 flowers in each bouquet.
2. First I found the factors of 51 and came up with 17 and 3, 3and 17, 51 and 1, and 1 and 51. So that means Ms.Warren can make 17 bouquets of 3 flowers, 3 bouquets of 17 flowers, 51 bouquets of 1 flower and 1 bouquet of 51 flowers.