Question

Under what conditions is the cost to develop a roll of film the same either store.

Short answer

The cost to develop a roll film is same at both stores when 3.3 rolls are used.

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 – Equate both the equations

The cost at both the labs is same when cost equations of both labs is equated.

Equate the equations $y=3.20x+8$ and $y=2.60x+10$.

$\begin{array}{c}3.20x+8=2.60x+10\\ 3.20x-2.60x=10-8\\ 0.6x=2\\ x=\frac{2}{0.6}\\ x=3.3\end{array}$

Since, x denote number of rolls so if both labs use 3.3 rolls then cost of developing a roll of film is same.

Thus, the cost at the Photo Lab and Specialty Photos is same when 3.3 rolls are used.