Question

When is it best to use The Photo Lab and when is it best to use Specialty Photos?

Short answer

When number of rolls are greaterthan 3.3 then it is best to use Specialty Photos and when number of rolls are less than 3.3 then it is best to use The Photo Lab.

Step-by-step solution

Step-1 – Interpret the data

According to the question, a roll of film is developed at two places.

The cost of developing a roll of film includes two things cost of roll and cost of print.

At the Photo Lab the cost is $3.20 per roll plus 8 per print.

At the Specialty Photos the cost is $2.60 per roll plus 10 per print.

Step-2 – Define the variables

Consider two variables x and y.

Denote the cost of each roll by x and total cost of developing the roll film by y.

Step-3 – Build the equations

Let the lab use x rolls.

At the Photo Lab the cost is $3.20 per roll plus $8$ per print.

Therefore, the cost of developing roll of film is expressed below.

$y=3.20x+8$

At the Specialty Photos the cost is $2.60 per roll plus 10 per print.

Therefore, the cost of developing roll of film is expressed below.

$y=2.60x+10$

Thus, the equations that represent cost of developing a roll of film are $y=3.20x+8$ and $y=2.60x+10$ at the Photo Lab and Specialty Photos respectively.

Step-4 – Graph the equations

Graph the equations that represent cost of developing a roll of film are $y=3.20x+8$and $y=2.60x+10$at the Photo Lab and Specialty Photos respectively.

The blue line represent the equation $y=3.20x+8$ and green line represent the equation represent $y=2.60x+10$.

Step-5 – Break-even point 

Both the equations intersect at the point $\left(3.3,18.6\right)$. This is the break-even point.

When number of rolls are greater than 3.3 then it is best to use Specialty Photos and when number of rolls are less than 3.3 then it is best to use The Photo Lab.