Question

Jenny, the florist had 72 roses,27 glodioli, and 54 marigold to be used to make bouqent. She has to make identical bouqents having all three varities of flower. What is the maximum numbers of identical bouqents that jenny can make if she uses all the flowers?

Answer 1

Given:

• Number of roses Jenny had = 72
• Number of gladioli she had = 27
• Number of marigold she had = 54

To find:

Maximum number of identical bouquets that Jenny can make using all the flowers

Solution:

→ The question mentions that Jenny has to make bouquets having all three  given flowers, and the bouquets should be identical. All the flowers will have to be used in making the bouquets and there should be no leftover.

→ That means, we have to find a number that completely divides all the given numbers of flowers. Also, did you notice? There is a "maximum" word in the question, which relates to the word "highest". Ultimately, we mean to find the Highest Common Factor or HCF of the numbers 72, 27 and 54.

→ Let's prime factorize the numbers.

$\Large{ \begin{array}{c|c} \tt 2 & \sf{ 72} \\ \cline{1-2} \tt 2 & \sf { 36} \\ \cline{1-2} \tt 2 & \sf{ 18} \\ \cline{1-2} \tt 3 & \sf{ 9} \\ \cline{1-2} \tt 3 & \sf{ 3 }\\ \cline{1-2} & \sf{ 1} \end{array}}$

• Prime factorization of 72 = 2 x 2 x 2 x 3 x 3

$\Large{ \begin{array}{c|c} \tt 3 & \sf{ 27} \\ \cline{1-2} \tt 3 & \sf { 9} \\ \cline{1-2} \tt 3 & \sf{ 3} \\ \cline{1-2} & \sf{ 1} \end{array}}$

• Prime factorization of 27 = 3 x 3 x 3

$\Large{ \begin{array}{c|c} \tt 2 & \sf{ 54} \\ \cline{1-2} \tt 3 & \sf { 27} \\ \cline{1-2} \tt 3 & \sf{ 9} \\ \cline{1-2} \tt 3 & \sf{ 3} \\ \cline{1-2} & \sf{ 1} \end{array}}$

• Prime factorization of 54 = 2 x 3 x 3 x 3

→ HCF of 72, 27, 54 = 3 x 3 = 9

Therefore, 9 is the maximum number of identical bouquets that Jenny can make using all the flowers.

So, 72/9 = 8 roses in a bouquet among other replicas.

27/9 = 3 gladioli in a bouquet among other replicas.

54/9 = 6 marigold in a bouquet among other replicas.

Kindly check the attachments if the factorizations are not making sense. :)