The ratio of roses and lilies in a garden is 3:2 respectively. The average number of roses and lilies is 180. What is the number of lilies in the garden?

To solve this problem, we need to understand that the ratio given (3:2) represents the distribution of roses to lilies in the garden.

Step 1: Add the two parts of the ratio together. 3 (for roses) + 2 (for lilies) = 5 parts in total.

Step 2: The average number of roses and lilies is given as 180. This means that the total number of flowers (roses + lilies) in the garden is 180 * 2 = 360.

Step 3: Now, we know that the 5 parts (from the ratio) represent 360 flowers. So, 1 part represents 360 / 5 = 72 flowers.

Step 4: The number of lilies is represented by 2 parts (from the ratio). So, the number of lilies in the garden is 2 * 72 = 144.

So, there are 144 lilies in the garden.