Pristine Printing will print business cards for $.10 each plus a setup charge of $15. The Printing Place offers business cards for $.15 each with a setup charge of $10. What number of business cards costs the same from either printer?

For 100 cards, the costs will be the same.
Define the variable first.
Let the number of cards be ##x##
For each printer, the calculation process is the same, just using different values.
At Pristine P. Cost of ##x## cards is: ##0.10xx x + 15 = color(blue)(0.10x +15)##
(10c per card plus set up charge of $15)
At Printing P : Cost of ##x## cards is: ## 0.15xx x + 10 =color(red)(0.15x+10)##
(15c per card plus set up charge of $10)
For ##x## cards, the two costs will be the same:
##color(red)(0.15x +10) = color(blue)(0.10x+15)##
##0.15x-0.10x = 15-10##
##0.05x = 5##
##x = 5/0.05##
##x = 100##