Mrs. william is deciding between two field tips for her class. The science center charges $135 plus $3 per student. The dino discovery museum simply charges $6 per student. For how many students will the science center charge less than the dino discovery museum?
Let x be the number of student going to the field trio.
Cost = fixed cost + variable cost
Cost for the science center
Fixed cost = 135
Variable cost = 3 × x
Cost = 135 + 3x
Cost for the dino discovery
Fixed cost = 0
Variable cost = 6x
The science center will charge less than the dino center if
135 + 3x < 6x
135 + 3x - 3x < 6x - 3x
135 + 0 < 3x
135 < 3x
Divide both sides by 3
135 / 3 < 3x / 3
45 < x
x > 45
The science center will charge less than the dino center if the number of students going is bigger than 45