Question

Ms. Chen is planning to take her camp group on a field trip to Pottery Bayou where each person will create her own piece of art pottery. The regular cost is $19 per person. There is a group special that costs $12 per person with an additional $84 fee for a private room. Ms. Chen is trying to decide if she should use the regular price or the group special.
(Part 1)Write an equation to show the total cost of the regular price with x people.


(Part 2)Write an equation to show the total cost of the group special with x people.

(Part 3)Graph the equations

(Part 4) When would the two admission prices be the same?

(Part 5)How much would it cost to bring 8 people on the field trip for the regular price, and how much for the group special?

(Part 6)When would it be better to go with the regular price and when would it be better to go with the group special?

(Part 7)The director of the camp told Ms. Chen that she can have a budget of $150 to bring as many campers as she can. Which deal should Ms. Chen go with and what is the maximum number of people she can bring with $150?



*Use what you know about solving systems of equations to help Ms. Chen solve her dilemma.You may use those equations in helping you solve this problem. Please complete all answers, and if you could give a brief explanation, if you can. *

Answer 1

Answer:Let x represent the number of people

:

A) Regular Cost = 40x

:

B) Group Cost = 25x + 150

:

C) equation graph A is the red line, B is the green line

x axis(each tick mark is one person), y axis(each tick mark is $100)

+graph%28+300%2C+200%2C+0%2C+15%2C+0%2C+600%2C+40x%2C+25%2Ax+%2B150%29+

:

D) The admission prices are the same when there are 10

people and the cost is $400

:

E) 6 people, regular price = 40 * 6 = $240

6 people, group price = (25 * 6) + 150 = $300  

 

:

F) We look at the graph of the two cost functions

The regular cost function is cheaper when we have less than 10 people

The group cost is cheaper when we have more than 10 people

:

G) we solve each cost function for x when the cost is $300

40x = 300

:

x = 7.5 people

:

25x + 150 = 300

25x = 150

x = 6

:

regular price allows us to bring 7 people, one person more than group price

Hope this helps! ~ Autumn :)