A flower shop just received a shipment of flowers. The table shows the number of each type.

Question

A 2-column table with 5 rows. Column 1 is labeled Type of flower with entries lilies, daisies, carnations, asters, daffodils. Column 2 is labeled Amount with entries 60, 36, 72, 42, 24.

The florist selects from these flowers to make arrangements for the upcoming flower show.

Use the drop-down menus to complete the statements.

The greatest number of identical arrangements that can be made using only the carnations and asters with no flowers left over is
.
The greatest number of identical arrangements that can be made using only the lilies and daffodils with no flowers left over is
.

Answer 1

To find the greatest number of identical arrangements that can be made with no flowers left over using only specific types of flowers, we need to calculate the greatest common divisor (GCD) of the amounts for the flowers in each category.

1. For carnations (72) and asters (42):

   • The amounts are 72 and 42.
   • The factors of 72 are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.
   • The factors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42.
   • The common factors are: 1, 2, 3, 6.
   • The greatest common factor is 6.

2. For lilies (60) and daffodils (24):

   • The amounts are 60 and 24.
   • The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
   • The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24.
   • The common factors are: 1, 2, 3, 4, 6, 12.
   • The greatest common factor is 12.

So, the completed statements are:

• The greatest number of identical arrangements that can be made using only the carnations and asters with no flowers left over is 6.
• The greatest number of identical arrangements that can be made using only the lilies and daffodils with no flowers left over is 12.