Dunder Mifflin will print business cards for $0.10 each plus setup charge of $15. Werham Hogg offers

Dunder Mifflin will print business cards for $0.10 each plus setup charge of $15. Werham Hogg offers business cards for $0.15 each with a setup charge of $10. What numbers of business cards cost the same from either company

Declare variables:

• Let b be the number of business cards.

Set up the cost function C(b) for Dunder Mifflin:
C(b) = Cost to print each business card * b + Setup Charge
C(b) = 0.1b + 15

Set up the cost function C(b) for Werham Hogg:
C(b) = Cost to print each business card * b + Setup Charge
C(b) = 0.15b + 10

The phrase cost the same means we set both C(b)'s equal to each other and solve for b:
0.1b + 15 = 0.15b + 10

Solve for b in the equation 0.1b + 15 = 0.15b + 10

Step 1: Group variables:
We need to group our variables 0.1b and 0.15b. To do that, we subtract 0.15b from both sides
0.1b + 15 - 0.15b = 0.15b + 10 - 0.15b

Step 2: Cancel 0.15b on the right side:
-0.05b + 15 = 10

Step 3: Group constants:
We need to group our constants 15 and 10. To do that, we subtract 15 from both sides
-0.05b + 15 - 15 = 10 - 15

Step 4: Cancel 15 on the left side:
-0.05b = -5

Step 5: Divide each side of the equation by -0.05
-0.05b/-0.05 = -5/-0.05
b = 100