There are 8 flowers in a garden. Some insects (butterflies and dragonflies) sit on flowers. There is no more than one insect per flower. More than half of the flowers are occupied. The number of butterflies on the flowers is twice the number of dragonflies on the flowers. How many butterflies sit on the flowers?

4 butterflies.

Step-by-step explanation:

Let x be the number of dragonflies, then the number of butterflies = 2x.

As more than half the flowers are occupied by 1 insect:

2x + x > 5.

3x > 5

x > 5/3.

If x = 2 then there are 4 butterflies and 6 of the flowers are occupied.

If x = 3 there are 6 butterflies and 9 flowers are occupied, but there are only 8 flowers, therefore the answer is 4 butterflies.

4

Step-by-step explanation:

x butterflies and y dragonflies

4 < x + y " 8

x = 2y

4 < 2y + y < 8

4 < 3y < 8

Only multiple of 2 between 4 and 8 is 6

So 3y = 6

y = 2

x = 2y = 4