Jhon's flower Flower problem? and Origami Flowers

Jhon's flower Flower problem?

Jhon received at least 100 flowers from an admirer. When he tried to place 5 flowers in each vase, he found that she had 4 flowers left over.When he tried to place 6 flowers in each vase, he found that she had 3 flowers left over.
What is the smallest number of roses he could have received?


flower best answer:

Answer by Thierry
Let n be the number of flowers.
The conditions are:
(1) n>=100 (n integer)
(2) There is k integer such as n=5k+4
(3) There is l integer such as n=6l+3

From (2): 6n=30k+24 (2')
From (3): 5n= 30l+15 (3')

(2')-(3'): n=30(k-l) + 9

So n is a multiple of 30 plus 9.
100=3*30+10
Hence 100+20+9 is the smallest number ar least equal to 100 that is equal to a multiple of 30 plus 9.
129 is your answer.

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Flowers I made for my mum's 60th birthday

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