Jasmine needs to make a bouquet of 24 yellow and orange carnations. The ratio of yellow carnations to all of the carnations must be 1 to 3. She determines that she will need 8 orange carnations for the bouquet. Which statement correctly describes her error?

Question

She did not include enough orange carnations. She thought the ratio of orange carnations to all carnations was 1 to 3.
She included too many orange carnations. If 1 of the 3 flowers is yellow, then 2 must be orange.
She did not include enough orange carnations. If 1 of the 24 flowers is yellow, then 23 must be orange.
She included too many orange carnations. She thought the ratio of orange carnations to yellow carnations was 1 to 3.

Answer 1

To analyze Jasmine's situation, we start with the information given:

• Jasmine wants a total of 24 carnations.
• The ratio of yellow carnations to all carnations must be 1 to 3.

From the ratio of yellow flowers to all flowers, we can conclude:

• For every 1 yellow carnation, there are 3 total carnations.
• Therefore, if we let \( y \) represent the number of yellow carnations, then: \[ y + o = 24 \] where \( o \) is the number of orange carnations.

Since the ratio of yellow to total is 1 to 3: \[ \frac{y}{24} = \frac{1}{3} \] To find \( y \), we can cross-multiply: \[ 3y = 24 \implies y = \frac{24}{3} = 8 \] This means Jasmine needs to have 8 yellow carnations.

To find the number of orange carnations \( o \): \[ o = 24 - y = 24 - 8 = 16 \] So Jasmine needs 16 orange carnations.

However, Jasmine states that she thinks she will need 8 orange carnations, which is incorrect since she actually needs 16 orange carnations.

Reviewing the statements:

1. She did not include enough orange carnations. She thought the ratio of orange carnations to all carnations was 1 to 3. - This is incorrect because she miscalculated the number of orange carnations, but her thought about the ratio pertains to yellow to total.
2. She included too many orange carnations. If 1 of the 3 flowers is yellow, then 2 must be orange. - This is incorrect because when correctly applying the ratio, there should be 16 orange carnations.
3. She did not include enough orange carnations. If 1 of the 24 flowers is yellow, then 23 must be orange. - This is clearly wrong since we determined she needs 8 yellow and 16 orange.
4. She included too many orange carnations. She thought the ratio of orange carnations to yellow carnations was 1 to 3. - This is incorrect because she actually thought she needed 8 orange, not that it was too many.

The only correct conclusion is that Jasmine made an error in calculating the number of orange carnations needed, incorrectly concluding she only needed 8, instead of the correct 16. Thus, the correct statement would more closely align with acknowledging she did not include enough orange carnations.

Thus, the most fitting description of her error is the first option: She did not include enough orange carnations. She thought the ratio of orange carnations to all carnations was 1 to 3. Although a small detail in correctness about interpreting the ratios, this aligns with her misunderstanding of the proper counts.