SOLUTION: 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 $20 per person. There i
Question 1110683: 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 $20 per person. There is a group special that costs $10 per person with an additional $50 fee for a private room. Ms. Chen is trying to decide if she should use the regular price or the group special.
A) Write an equation to show the total cost of the regular price with x people.
B) Write an equation to show the total cost of the group special with x people.
C) Graph the equations
D) When would the two admission prices be the same? Explain how you know this using 1-2 complete sentences.
E) How much would it cost to bring 6 people on the field trip for the regular price, and how much for the group special? Explain how you know this using 1-2 complete sentences.
F) When would it be better to go with the regular price and when would it be better to go with the group special? Explain how you know this using 1-2 complete sentences. (2 points)
G) The director of the camp told Ms. Chen that she can have a budget of $150 to bring as many campers as she can. What deal should Ms. Chen go with and what is the maximum number of people she can bring with $150? Support your answer by showing how many people can go with each deal using 2-3 complete sentences.
special cost is 50 plus 10 per person, therefore 50 + 10x
questions and answers shown below:
A) Write an equation to show the total cost of the regular price with x people.
cost = 20x
B) Write an equation to show the total cost of the group special with x people.
cost = 50 + 10x
C) Graph the equations
D) When would the two admission prices be the same? Explain how you know this using 1-2 complete sentences.
the admission prices would be the same when 5 people go.
the regular admission price is 20 * 5 = 100
the special admission price is 50 + 10 * 5 = 100.
the graph shows the break even point.
E) How much would it cost to bring 6 people on the field trip for the regular price, and how much for the group special? Explain how you know this using 1-2 complete sentences.
the regular admission price is 20 * 6 = 120
the special price is 50 + 10 * y = 110
the special price is less.
F) When would it be better to go with the regular price and when would it be better to go with the group special? Explain how you know this using 1-2 complete sentences. (2 points)
the break even point is 5 people.
any number of people greater than 5 would be cheaper with the special price.
any number of people less than 5 would be cheaper with the regular price.
you find this out by checking the prices with 4 people and checking the prices with 6 people.
you can also turn your cost equations into inequalities.
break even is when 20x = 50 + 10x
standard price is cheaper when 20x < 50 + 10x.
special price is chaeper when 50 + x < 20x.
solving for standard price being cheaper gets you x < 5.
start with 20x < 50 + 10x
subtract 10x from both sides to get 10x < 50
divide both sides by 10 to get x < 5
solving for special price being cheaper gets you x > 5.
start with 50 + 10x < 20x
subtract 10x from both sides to get 50 < 10x
divide both sides by 10 to get 5 < x
this is the same as x > 5.
G) The director of the camp told Ms. Chen that she can have a budget of $150 to bring as many campers as she can. What deal should Ms. Chen go with and what is the maximum number of people she can bring with $150? Support your answer by showing how many people can go with each deal using 2-3 complete sentences.
set the cost equal to 150 and solve each equation.
with standard pricing, 150 = 20x.
solve for x to get x = 150/20 = 7.5
round down to 7.
with special pricing, 150 = 50 + 10x
subtract 50 from both sides to get 100 = 10x
solve for x to get x = 100/10 = 10
10 people can go with special pricing and only 7 people can go with regular pricing.
