Question

A photographer store sells sampler A consisting of 6 rolls of color film and 4 rolls of black and white film for $82. It also sells sampler B, consisting of 4 rolls of color film and 6 rolls of black and white film for $68. What is the cost per roll of each type of film?

Option 1: Color film costs $7 per roll, and black and white film costs $9 per roll.
Option 2: Color film costs $8 per roll, and black and white film costs $6 per roll.
Option 3: Color film costs $10 per roll, and black and white film costs $5 per roll.
Option 4: Color film costs $6 per roll, and black and white film costs $7 per roll.

Answer 1

By solving a system of equations derived from the prices of sampler packages, we deduced that the cost per roll of color film is $10 and the cost per roll of black and white film is $5, indicating that Option 3 is the correct answer.

Step-by-step explanation:

The question provided requires solving a linear system of equations to determine the cost per roll of each type of film, that is, color film and black and white film. By setting up the two equations based on the given sampler packages and their prices, we can solve for the price of each type of film roll. The equations are as follows:

• 
  
• 6C + 4B = $82 for Sampler A
• 
  
• 4C + 6B = $68 for Sampler B

By using the method of substitution or elimination (such as multiplying the first equation by 2 and the second by 3, then subtracting them), we can solve for the variable C, which represents the cost of a roll of color film, and B, the cost of a roll of black and white film.

After solving this system of equations, we find that the cost per roll of color film is $10 and the cost per roll of black and white film is $5. Thus, Option 3 is the correct answer: Color film costs $10 per roll, and black and white film costs $5 per roll.