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The problem describes two printing services and their pricing structures for business cards:

1. **Pristine Printing** charges $0.10 per card and a setup fee of $15.
2. **The Printing Place** charges $0.15 per card and a setup fee of $10.

The task is to find the number of business cards for which the total cost from both printers is the same.

Let's denote the number of business cards by $ x $.

The total cost for Pristine Printing is:
\[
\text{Cost for Pristine Printing} = 0.10x + 15
\]

The total cost for The Printing Place is:
\[
\text{Cost for The Printing Place} = 0.15x + 10
\]

To find the number of cards where the costs are equal, we set these two equations equal to each other:
\[
0.10x + 15 = 0.15x + 10
\]

Now, let's solve for $ x $:

\[
15 - 10 = 0.15x - 0.10x
\]

\[
5 = 0.05x
\]

\[
x = \frac{5}{0.05} = 100
\]

So, **100 business cards** will cost the same at both Pristine Printing and The Printing Place.

Would you like further details or have any questions? Here are some related questions you might consider:

1. How would the solution change if the setup charge for one of the printers was different?
2. What would be the cost for 100 business cards at each printer?
3. How does the cost per card affect the break-even point?
4. What if you needed 150 cards—how would the costs compare then?
5. Can you derive a general formula for the break-even point between two printers with different cost structures?

**Tip:** When comparing pricing models with fixed and variable costs, setting the total cost equations equal to each other helps identify the break-even point.

Pristine Printing will print business cards for $0.10 each plus a setup charge of $15. The Printing Place offers business cards for $0.15 each with a setup charge of $10. What number of business cards costs the same from either printer?

Find out how to determine the number of business cards that result in the same cost from two different printing services. This algebra problem involves solving linear equations and is suitable for students in Grades 6-8.

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