Answer:
A)
Adventureland.
B)
Coaster City
C)
5 People
Step-by-step explanation:
The cost of Adventureland for p people is:
[tex]A=20+9p[/tex]
And the cost of Coaster City for p people is:
[tex]C=40+5p[/tex]
Part A)
If four people is going on the trip, p = 4. So, the cost for Adventureland is:
[tex]20 + 9(4) = \$ 56[/tex]
And the cost for Coaster City is:
[tex]40+5(4)=\$60[/tex]
Since $56 < $60, Adventureland will be a better option.
Part B)
If three extra people were invited, the total amount of people p is now 7. So, the cost to Adventureland is:
[tex]20 + 9(7) = \$ 83[/tex]
And the cost to Coaster City is:
[tex]40+5(7)=\$ 75[/tex]
Since $75 < $83, Coaster City is the better option in this case.
Part C)
So, we can set the two cost equations equal to each other:
[tex]20+9p=40+5p[/tex]
Solve for p. Subtracting 20 from both sides yields:
[tex]9p=20+5p[/tex]
And subtracting 5p from both sides yields:
[tex]4p=20[/tex]
And dividing both sides by 4:
[tex]p=5[/tex]
So, if 5 people went on a trip, the cost of going to either Adventureland or Coaster City will be the same.
