Jana 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, Jana 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 Jana has to work with?
With the number of flowers determined above, how many bouquets or corsages and of what size can Jana make?
Do you think that Jana 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 - Jana doesn't want to waste a single flower.)
12 comments:
1.By adding the extras I have found out that the total amount of flowers ahe can put in each bouquet is 8
2.NO I do not .
mb
J.M.
There are 51 left over flowers. 4x12 is 48 plus 3 = 51. 7x7 is 49 plus 2 = 51. 8x6 is 48 plus 3 = 51.
# of Bouquets 7 flowers 4 flowers 8 flowers
7
14
21
28
35
42
49
2 left over 4
8
12
16
20
24
28
32
36
40
44
48
3 left over 8
16
24
32
40
48
3 left over
All of those equal 51. 7x7 =49 plus 2 = 51. 3x17=51 so she can make 3 bouquets of 17 flowers, or she could have 17 bouquets of 3 flowers each.
MJS
#Bouquets 7 Flowers each 8 Flowers each 4 Flowers each
1
2
3
4
5
6
7
8
9
10
11
12 7
14
21
28
35
42
49
2 left over 8
16
24
32
40
48
3 left over 4
8
12
16
20
24
28
32
36
40
44
48
3 left over
There are 51 flowers left over from last sale. 7x7= 49 with the remainder of 2 like it says.
I you do 8x6= 48. That leaves 3 left. 4x12= 48. All those left over are the left over’s said in the blog.
She can have it where there are no flowers left over. She could have 3 Bouquets of 17 flowers or 17 Bouquets of three flowers.
J.M.
There are 51 left over flowers. 4x12 is 48 plus 3 = 51. 7x7 is 49 plus 2 = 51. 8x6 is 48 plus 3 = 51.
# of Bouquets 7 flowers 4 flowers 8 flowers
1
2
3
4
5
6
7
8
9
10
11
12
7
14
21
28
35
42
49
2 left over 4
8
12
16
20
24
28
32
36
40
44
48
3 left over 8
16
24
32
40
48
3 left over
All of those equal 51. 7x7 =49 plus 2 = 51. 3x17=51 so she can make 3 bouquets of 17 flowers, or she could have 17 bouquets of 3 flowers each.
AM
7 4 8
14 8 16
21 12 24
28 16 32
35 20 40
42 24 48
49 28 56
56 32
36
40
44
48
52
56
8 14 7
1. The smallest number Jana can work with is 56 flowers. It is 56 because 4 multiplied by 14 is 56. Also 8 multiplied by 7 is 56. Finally 7 multiplied by 7 is 56. Since all of these numbers go into 56 the lowest common multiple is 56.
2. The number of flower group can be 14, 8 and 7. Those are the banquets because if she makes of 4 banquets there would be 14 banquets of 4, if she used 8 flowers for the banquets size she would have 7 groups, if she had 7 flowers in a banquets she would have 8 banquets of flowers.
3. Yes, because if she had at least the LCM of the three she could make those size of banquets.
TM
1. The smallest number Jana can work with is 56. It is 56 because the lowest common multiple of 4, 7, and 8 is 56, therefore the smallest number she can use where all these will go into without there being a leftover flower.
2. If Jana used 4 per banquet she could make 14 banquets, if she used 7 flowers per banquet she could make 8 banquets, if she used 8 flowers per banquet she could make 7 banquets.
3. Yes, because if she had at least the lowest common multiple of all three she could make banquets without wasting any flowers or if she had any multiple of all three she could do it.
WO
The least number would be 56 because 4, 7, and 8 all can go into that number.
She could make a bouquet or corsage with 1 flower in 56 b/c, 2 flowers in 28 b/c, 4 flowers in 28 b/c, 7 flowers in 8 b/c, and the opposite of all these factors.
I think that Jana could use numbers other than 7, 8, and 4 if she had more or less left over’s, which could change the result.
c/b = corsage and bouquet
MG
Fifty one, seven goes closest by going to forty nine, which has two left over. Then there’s eight, which goes closest by going to forty eight, with three left over. Eight and four can go into forty eight, which is the highest they can go without going over fifty one.
Seventeen can make three bouquets because seventeen multiplied by three is fifty one or one big bouquet of fifty one flowers.
7 x 7= 49, two left over because 51-49 = 2.
8x 6= 48, three left over because 51- 48 = 3.
17 x 3= 51. 3 bouquets of flowers or 51 x 1= 51.
SK
4=3left
7=2left
8=3left
1.
4 8 12 16 20 24+3=27
7 14 21 \
4 7 8
7
11
15
19
23
27
31
35
39
43
47
51 9
16
23
30
37
44
51 11
19
27
35
43
51
For the number of leftovers specified in the question, Jana would have to have 51 flowers. I figured this out by making a table. For each number in the bouquets, I added the leftover number, and then continued to add the original. Once it was complete, I looked for the similar number. The lowest one was 51, thus I had my answer.
2. Jana could make 17 bouquets of three. I figured this out by dividing 51 by 3, and the answer was 17. Thus, 17 was the number of bouquets, and 3 was the number of flowers in each.
3.
7
14
21
28
35
42
49
56
63
70
8
16
24
32
40
48
56
64
72
80 9
18
27
36
45
54
63
72
81
90
After a brief chart of the multiples, I have found myself coming to the conclusion that they will never land on the same number.
CB
4=3left
7=2left
8=3left
1.
4 8 12 16 20 24+3=27
7 14 21 \
4 7 8
7
11
15
19
23
27
31
35
39
43
47
51 9
16
23
30
37
44
51 11
19
27
35
43
51
For the number of leftovers specified in the question, Jana would have to have 51 flowers. I figured this out by making a table. For each number in the bouquets, I added the leftover number, and then continued to add the original. Once it was complete, I looked for the similar number. The lowest one was 51, thus I had my answer.
2. Jana could make 17 bouquets of three. I figured this out by dividing 51 by 3, and the answer was 17. Thus, 17 was the number of bouquets, and 3 was the number of flowers in each.
3.
7
14
21
28
35
42
49
56
63
70
8
16
24
32
40
48
56
64
72
80 9
18
27
36
45
54
63
72
81
90
After a brief chart of the multiples, I have found myself coming to the conclusion that they will never land on the same number.
R.T
1. The smallest possible number of flowers is 56. It is 56 because the lowest common multiple of 4, 7, and 8 is 56, therefore the smallest number she can use where all these will go into without there being a leftover flower.
2. If Jana used 4 flowers per banquet she could make 14 banquets, if she used 7 flowers per banquet she could make 8 banquets, if she used 8 flowers per banquet she could make 7 banquets.
3. Yes, because if she had at least the lowest common multiple of all three she could make banquets without wasting any flowers or if she had any multiple of all three she could do it.
MG
Fifty one, seven goes closest by going to forty nine, which has two left over. Then there’s eight, which goes closest by going to forty eight, with three left over. Eight and four can go into forty eight, which is the highest they can go without going over fifty one.
Seventeen can make three bouquets because seventeen multiplied by three is fifty one or one big bouquet of fifty one flowers.
7 x 7= 49, two left over because 51-49 = 2.
8x 6= 48, three left over because 51- 48 = 3.
17 x 3= 51. 3 bouquets of flowers or 51 x 1= 51.
Yes, I do think it would be possible that she would have enough leftovers that it wouldn't matter if she chose to make bouquets of 7, 8, or 9.
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