In Katy’s garden there are 105 ladybugs. They are increasing at two ladybugs per month. There are currently 175 aphids and the number of aphids is decreasing at three aphids per month. When will the number of ladybugs and aphids in Katy’s garden be the same? Can you please explain step bye step.

They won't ever be the same at the same time.

explanation:

Add 2 to 150 and subtract 3 from 175 till you hit a common number at the same month

150, 152, 154, 156, 158, 160, 162

175, 173, 170, 169, 166, 163, 160

seeing as they have already passed each other, its not possible for the numbers to be the same at the same time.

linear pair postulates