The florist can order roses in bunches of one dozen and lilies in bunches of 8. Last month she ordered the same number of roses as lilies. If she ordered no more than 100 roses, how many bunches of each could she have ordered? What is the smallest number of bunches of each that she could have ordered? Explain your reasoning.
The florist could have ordered any multiple of 12 roses that is less than 100:
12, 24, 36, 48, 60, 72, 84, or 96.
The florist could have ordered any multiple of 8 lilies that is less than 100:
8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96
If she ordered the same number of each kind of flower, she must have ordered a common multiple of 8 and 12, shown in the table below:
| Number of each kind of flower | 24 | 48 | 72 | 96 |
|---|---|---|---|---|
| Number of bunches of roses | 2 | 4 | 6 | 8 |
| Number of bunches of lilies | 3 | 6 | 9 | 12 |
The number of bunches of each are shown in the second and third rows. We can find the number of bunches of roses by dividing the number of flowers by 12, and we can find the number of bunches of lilies by dividing the number of flowers by 8.
The smallest number of each she could have ordered was 2 bunches of roses and 3 bunches of lilies.
Commentary
This task provides a context for some of the questions asked in "6.NS Multiples and Common Multiples." A scaffolded version of this task could be adapted into a teaching task that could help motivate the need for the concept of a common multiple.