Chapter 4.2, Problem 33E

To determine

To calculate: The greatest number of identical bouquets. Also find number of flowers that each bouquet contain.

Answer to Problem 33E

7 bouquets can be made. Each bouquet contains 9 daisies, 8 lilies, 6irises and 3 freesias.

Explanation of Solution

Given information:

Given graph is,

  

Consider the graph as,

  

According to the graph there are 63 daisies, 56 lilies, 42 irises and 21 freesias.

Now, 63 can be written as,

  $\begin{array}{c}63=3\times 21\\ =3\times 3\times 7\end{array}$

56 can be written as,

  $\begin{array}{c}56=2\times 28\\ =2\times 2\times 14\\ =2\times 2\times 2\times 7\end{array}$

42 can be written as,

  $\begin{array}{c}42=2\times 21\\ =2\times 3\times 7\end{array}$

21 can be written as,

  $21=3\times 7$

The greatest common factor of $63,56,42\text{ and }21$ is $7$

Hence, 7 bouquets can be made.

A bouquet contains $\frac{63}{7}=9$ daisies, $\frac{56}{7}=8$ lilies, $\frac{42}{7}=6$ irises and $\frac{21}{7}=3$ freesias.

Therefore, 7 bouquets can be made. Each bouquet contains 9 daisies, 8 lilies, 6irises and 3 freesias.