When you get home to plant the flowers, you have 3 different flowerbeds where you plan on planting flowers.

You have two flowerbeds where you want the same ratio for tulips to geraniums.

In one of these flowerbeds, you have 4 tulips and 3 geraniums.

In the other flowerbed, you have 6 geraniums.

- How many tulips should there be in the second flowerbed to have the same ratio of tulips to geraniums as the first flowerbed?

- How many total geranium flowers are used in these two flowerbeds?

- How many total tulip flowers are to be used in these two flowerbeds?

- How many of each do we have left to use in the remaining flowerbed?

The second flowerbed requires 8 tulips to maintain the same ratio as the first. There will be a total of 9 geraniums and 12 tulips in both flowerbeds.

To maintain the same ratio of tulips to geraniums as in the first flowerbed, which has 4 tulips and 3 geraniums, we should set up a proportion. The ratio is 4 tulips to 3 geraniums, or 4:3. In the second flowerbed, we have 6 geraniums, so we set up the proportion 4/3 = x/6, where x is the number of tulips needed in the second flowerbed.

By cross-multiplying, we get 3x = 24, thus x = 8. So, the second flowerbed needs 8 tulips.

The total number of geraniums in both flowerbeds is 3 in the first plus 6 in the second, totaling 9 geraniums.

The total number of tulips needed for both flowerbeds is 4 in the first plus 8 in the second, totaling 12 tulips.

If we have a specific number of flowers to begin with, we can determine how many are left for the remaining bed by subtracting the number already used in the first two beds from the initial quantity.