Question

A florist can order roses in bunches of 12 and lilies in bunches of 8. Last month she ordered the same number of roses and lilies. If she ordered no more than 100 of each kind of flower, how many bunches of each could she have ordered? Find all the possible combinations.

Answer 1

2 bunches of roses and 3 bunches of lilies.

4 bunches of roses and 6 bunches of lilies.

Explanation:

Given that:

Roses come in a bunch of 12 flowers and

Lilies come in a bunch of 8 flowers

Number of roses ordered is equal to the number of lilies ordered.

Total number of flowers ordered are lesser than 100.

To find:

The possible number of combinations such that equal number of flowers are bought.

Solution:

Here, we need to find the Least Common Multiple.

`12 = \underline{2 * 2} * 3`

`8 = \underline{2 * 2} * 2`

LCM =
`2* 2 * 3 * 2 = 24`

Therefore, we need to find the number of bunches such that number of flowers of each type bought are equal to LCM or multiples of LCM.

i.e.

24, 48, 72, 96 ....

Here, two types of flowers are there.

Therefore, 24 of each type, total 48 flowers i.e. 2 bunches of roses and 3 bunches of lilies.

48 of each type, total 96 flowers i.e. 4 bunches of roses and 6 bunches of lilies.

Total possible combinations:

2 bunches of roses and 3 bunches of lilies.

4 bunches of roses and 6 bunches of lilies.