Sean can produce up to 692 grayscale brochures without exceeding his budget.
How to solve
Step 1: Define variables
grayscale_cost: Cost of producing one grayscale brochure ($0.02)
color_cost: Cost of producing one colored brochure ($0.08)
budget: Total monthly budget for brochures ($14.00)
grayscale_brochures: Number of grayscale brochures to be produced
color_brochures: Number of colored brochures to be produced
Step 2: Set up the equations
Equation 1: Total cost of brochures should not exceed the budget.
grayscale_cost * grayscale_brochures + color_cost * color_brochures <= budget
Substitute the values:
0.02 * grayscale_brochures + 0.08 * 2 <= 14.00
Equation 2: We know Sean wants to produce only two colored brochures:
color_brochures = 2
Step 3: Solve for grayscale brochures
Substitute the second equation into the first equation and solve for grayscale_brochures:
0.02 * grayscale_brochures + 0.08 * 2 <= 14.00
0.02 * grayscale_brochures + 0.16 <= 14.00
0.02 * grayscale_brochures <= 13.84
grayscale_brochures <= 13.84 / 0.02
grayscale_brochures <= 692
Therefore, Sean can produce up to 692 grayscale brochures without exceeding his budget.
The Complete Question
Sean plays the upright bass as part of a string quartet and advertises booking opportunities using brochures he distributes in venues around the city. Making one grayscale brochure costs $0.02, but adding color increases the cost to $0.08 per brochure. Sean sets aside a monthly budget of $14.00 for creating brochures.
how many grayscale brochures can he produce with his monthly budget if he adds color to only 2