The bouquet has 16 roses and 4
ilies. Write three ratios (part-to-
whole, whole-to-part, and
part-to-part) describing this
relationship.

Question

The bouquet has 16 roses and 4 ilies. Write three ratios (part-to- whole, whole-to-part, and part-to-part) describing this relationship.

UpStudy AI · Accepted Answer

To describe the relationship between the roses and lilies in the bouquet, we can define the following ratios:

1. **Part-to-Whole Ratio**: This ratio compares a part of the bouquet to the whole bouquet. Here, we can take the number of roses as the part.
   - Ratio of roses to the total number of flowers:
   $$
   \text{Part-to-Whole Ratio (Roses)} = \frac{16}{16 + 4} = \frac{16}{20} = \frac{4}{5}
   $$

2. **Whole-to-Part Ratio**: This ratio compares the whole bouquet to a part of it. We can take the total number of flowers to the number of roses.
   - Ratio of the total number of flowers to the number of roses:
   $$
   \text{Whole-to-Part Ratio (Roses)} = \frac{16 + 4}{16} = \frac{20}{16} = \frac{5}{4}
   $$

3. **Part-to-Part Ratio**: This ratio compares one part of the bouquet to another part. Here, we can compare the number of roses to the number of lilies.
   - Ratio of roses to lilies:
   $$
   \text{Part-to-Part Ratio (Roses to Lilies)} = \frac{16}{4} = 4
   $$

In summary, the ratios are:
- Part-to-Whole Ratio (Roses): $$ \frac{4}{5} $$
- Whole-to-Part Ratio (Roses): $$ \frac{5}{4} $$
- Part-to-Part Ratio (Roses to Lilies): $$ 4 $$
- Roses make up 4 out of every 5 flowers. - The total flowers are 5 times the number of roses. - There are 4 roses for every lily.

The bouquet has 16 roses and 4
ilies. Write three ratios (part-to-
whole, whole-to-part, and
part-to-part) describing this
relationship.

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