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##