After a busy day of orders, a florist has 6 roses, 7 lilies, 3 carnations, 35 chrysanthemums, 27 sunflowers, 18 violets, and 9 tulips left in her inventory.

Part A: Write a ratio that compares the number of roses to the number of violets.

Part B: Describe what three other comparisons have the same ratio.

Part C: Provide reasoning why more than one comparison can be made with the same ratio.

6/18 = 9/27 = 3/9

Can only find two others.

I'll let you provide the reasoning.

A ratio that compares the number of roses to the number of violets is 6:18 or 1:3. Three other comparisons are tulips to sunflowers, carnations to tulips,

Yeah what they said.

I agree!

Part A: To write a ratio comparing the number of roses to the number of violets, we need to determine the number of each flower. According to the information given, there are 6 roses and 18 violets remaining in the florist's inventory.

The ratio can be expressed as:

Roses : Violets = 6 : 18

Since both 6 and 18 are divisible by 6, we can simplify the ratio:

Roses : Violets = 1 : 3

Therefore, the ratio of roses to violets is 1:3.

Part B: Three other comparisons that have the same ratio as roses to violets are:

1. Lilies to Sunflowers: If we count the remaining flowers, we find that there are 7 lilies and 27 sunflowers. As both 7 and 27 are divisible by 7, we can simplify the ratio to 1:3, which is the same ratio as roses to violets.

2. Chrysanthemums to Tulips: By counting the remaining flowers, we see that there are 35 chrysanthemums and 9 tulips. Dividing both numbers by 7 gives us the simplified ratio of 5:1, which is the same as roses to violets.

3. Carnations to Violets: From the given information, we can see that there are 3 carnations and 18 violets. Dividing both numbers by 3 gives us the simplified ratio of 1:6, which is again the same as roses to violets.

Part C: More than one comparison can have the same ratio because ratios are a way to compare quantities, and there can be multiple quantities that have the same relative difference or proportion. In this case, all the comparisons in Part B have the same ratio as roses to violets but involve different combinations of flowers. This means that the relative proportion between the quantities remains the same, even though the actual values may differ. Ratios allow us to compare different quantities in a standardized way, regardless of the specific values being compared. Therefore, it is possible to find multiple comparisons that share the same ratio.