inequality and field trip

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

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