Brendan's older sisters, Angie and Alexa, are twins. For their graduation, he made each of them a bouquet of flowers. For Angie's bouquet, he used 6 lilies and 12 daisies. For Alexa's bouquet, he used 4 lilies and 14 daisies. Which bouquet had a lower ratio of lilies to daisies?

Answer 1

To find the ratio of lilies to daisies in each bouquet, we can calculate the ratios for Angie's and Alexa's bouquets separately.

Angie's bouquet:

• Lilies: 6
• Daisies: 12

The ratio of lilies to daisies is: \[ \text{Ratio}_\text{Angie} = \frac{\text{Lilies}}{\text{Daisies}} = \frac{6}{12} = \frac{1}{2} \]

Alexa's bouquet:

• Lilies: 4
• Daisies: 14

The ratio of lilies to daisies is: \[ \text{Ratio}_\text{Alexa} = \frac{\text{Lilies}}{\text{Daisies}} = \frac{4}{14} = \frac{2}{7} \]

Now, let's compare the two ratios, \(\frac{1}{2}\) and \(\frac{2}{7}\). To do this, we can convert both fractions to have a common denominator or convert them to decimals.

Using a common denominator:

• The least common multiple of 2 and 7 is 14.

• Convert \(\frac{1}{2}\): \[ \frac{1}{2} = \frac{7}{14} \]

• Convert \(\frac{2}{7}\): \[ \frac{2}{7} = \frac{4}{14} \]

Now we can compare:

• Angie's ratio: \(\frac{7}{14}\)
• Alexa's ratio: \(\frac{4}{14}\)

Since \(\frac{4}{14} < \frac{7}{14}\), Alexa's bouquet has a lower ratio of lilies to daisies.

Conclusion: Alexa's bouquet had a lower ratio of lilies to daisies.